Bibliography C
-
L. G. Cabral-Rosetti and M. A. Sanchis-Lozano (2000)
Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams.
J. Comput. Appl. Math. 115 (1-2), pp. 93–99.
-
F. Cajori (1929)
A History of Mathematical Notations, Volume II.
Open Court Publishing Company, Chicago.
-
N. Calkin, J. Davis, K. James, E. Perez, and C. Swannack (2007)
Computing the integer partition function.
Math. Comp. 76 (259), pp. 1619–1638.
-
F. Calogero (1978)
Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial as the index and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials.
Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.
-
J. Camacho, R. Guimerà, and L. A. N. Amaral (2002)
Analytical solution of a model for complex food webs.
Phys. Rev. E 65 (3), pp. (030901–1)–(030901–4).
-
P. J. Cameron (1994)
Combinatorics: Topics, Techniques, Algorithms.
Cambridge University Press, Cambridge.
-
J. B. Campbell (1979)
Bessel functions and of real order and real argument.
Comput. Phys. Comm. 18 (1), pp. 133–142.
-
J. B. Campbell (1980)
On Temme’s algorithm for the modified Bessel function of the third kind.
ACM Trans. Math. Software 6 (4), pp. 581–586.
-
J. B. Campbell (1981)
Bessel functions and of real order and complex argument.
Comput. Phys. Comm. 24 (1), pp. 97–105.
-
J. B. Campbell (1984)
Determination of -zeros of Hankel functions.
Comput. Phys. Comm. 32 (3), pp. 333–339.
-
R. Campbell (1955)
Théorie Générale de L’Équation de Mathieu et de quelques autres Équations différentielles de la mécanique.
Masson et Cie, Paris (French).
-
R. G. Campos (1995)
A quadrature formula for the Hankel transform.
Numer. Algorithms 9 (2), pp. 343–354.
-
S. M. Candel (1981)
An algorithm for the Fourier-Bessel transform.
Comput. Phys. Comm. 23 (4), pp. 343–353.
-
CAOP (website)
Work Group of Computational Mathematics, University of Kassel, Germany.
-
L. Carlitz (1953)
Some congruences for the Bernoulli numbers.
Amer. J. Math. 75 (1), pp. 163–172.
-
L. Carlitz (1954a)
-Bernoulli and Eulerian numbers.
Trans. Amer. Math. Soc. 76 (2), pp. 332–350.
-
L. Carlitz (1954b)
A note on Euler numbers and polynomials.
Nagoya Math. J. 7, pp. 35–43.
-
L. Carlitz (1958)
Expansions of -Bernoulli numbers.
Duke Math. J. 25 (2), pp. 355–364.
-
L. Carlitz (1960)
Note on Nörlund’s polynomial .
Proc. Amer. Math. Soc. 11 (3), pp. 452–455.
-
L. Carlitz (1961a)
A recurrence formula for .
Proc. Amer. Math. Soc. 12 (6), pp. 991–992.
-
L. Carlitz (1961b)
The Staudt-Clausen theorem.
Math. Mag. 34, pp. 131–146.
-
L. Carlitz (1963)
The inverse of the error function.
Pacific J. Math. 13 (2), pp. 459–470.
-
R. D. Carlitz (1972)
Hadronic matter at high density.
Phys. Rev. D 5 (12), pp. 3231–3242.
-
B. C. Carlson and J. FitzSimons (2000)
Reduction theorems for elliptic integrands with the square root of two quadratic factors.
J. Comput. Appl. Math. 118 (1-2), pp. 71–85.
-
B. C. Carlson and J. L. Gustafson (1994)
Asymptotic approximations for symmetric elliptic integrals.
SIAM J. Math. Anal. 25 (2), pp. 288–303.
-
B. C. Carlson and J. L. Gustafson (1985)
Asymptotic expansion of the first elliptic integral.
SIAM J. Math. Anal. 16 (5), pp. 1072–1092.
-
B. C. Carlson and J. M. Keller (1957)
Orthogonalization Procedures and the Localization of Wannier Functions.
Phys. Rev. 105, pp. 102–103.
-
B. C. Carlson and J. M. Keller (1961)
Eigenvalues of Density Matrices.
Phys. Rev. 121, pp. 659–661.
-
B. C. Carlson and E. M. Notis (1981)
Algorithm 577: Algorithm for incomplete elliptic intergrals [S21].
ACM Trans. Math. Software 7 (3), pp. 398–403.
-
B. C. Carlson and G. S. Rushbrooke (1950)
On the expansion of a Coulomb potential in spherical harmonics.
Proc. Cambridge Philos. Soc. 46, pp. 626–633.
-
B. C. Carlson (1961a)
Ellipsoidal distributions of charge or mass.
J. Mathematical Phys. 2, pp. 441–450.
-
B. C. Carlson (1961b)
Some series and bounds for incomplete elliptic integrals.
J. Math. and Phys. 40, pp. 125–134.
-
B. C. Carlson (1963)
Lauricella’s hypergeometric function .
J. Math. Anal. Appl. 7 (3), pp. 452–470.
-
B. C. Carlson (1964)
Normal elliptic integrals of the first and second kinds.
Duke Math. J. 31 (3), pp. 405–419.
-
B. C. Carlson (1965)
On computing elliptic integrals and functions.
J. Math. and Phys. 44, pp. 36–51.
-
B. C. Carlson (1966)
Some inequalities for hypergeometric functions.
Proc. Amer. Math. Soc. 17 (1), pp. 32–39.
-
B. C. Carlson (1970)
Inequalities for a symmetric elliptic integral.
Proc. Amer. Math. Soc. 25 (3), pp. 698–703.
-
B. C. Carlson (1971)
New proof of the addition theorem for Gegenbauer polynomials.
SIAM J. Math. Anal. 2, pp. 347–351.
-
B. C. Carlson (1972a)
An algorithm for computing logarithms and arctangents.
Math. Comp. 26 (118), pp. 543–549.
-
B. C. Carlson (1976)
Quadratic transformations of Appell functions.
SIAM J. Math. Anal. 7 (2), pp. 291–304.
-
B. C. Carlson (1977a)
Elliptic integrals of the first kind.
SIAM J. Math. Anal. 8 (2), pp. 231–242.
-
B. C. Carlson (1978)
Short proofs of three theorems on elliptic integrals.
SIAM J. Math. Anal. 9 (3), pp. 524–528.
-
B. C. Carlson (1979)
Computing elliptic integrals by duplication.
Numer. Math. 33 (1), pp. 1–16.
-
B. C. Carlson (1985)
The hypergeometric function and the -function near their branch points.
Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 63–89.
-
B. C. Carlson (1987)
A table of elliptic integrals of the second kind.
Math. Comp. 49 (180), pp. 595–606, S13–S17.
-
B. C. Carlson (1988)
A table of elliptic integrals of the third kind.
Math. Comp. 51 (183), pp. 267–280, S1–S5.
-
B. C. Carlson (1990)
Landen Transformations of Integrals.
In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.),
Lecture Notes in Pure and Appl. Math., Vol. 124, pp. 75–94.
-
B. C. Carlson (1995)
Numerical computation of real or complex elliptic integrals.
Numer. Algorithms 10 (1-2), pp. 13–26.
-
B. C. Carlson (1999)
Toward symbolic integration of elliptic integrals.
J. Symbolic Comput. 28 (6), pp. 739–753.
-
B. C. Carlson (2002)
Three improvements in reduction and computation of elliptic integrals.
J. Res. Nat. Inst. Standards Tech. 107 (5), pp. 413–418.
-
B. C. Carlson (2004)
Symmetry in c, d, n of Jacobian elliptic functions.
J. Math. Anal. Appl. 299 (1), pp. 242–253.
-
B. C. Carlson (2005)
Jacobian elliptic functions as inverses of an integral.
J. Comput. Appl. Math. 174 (2), pp. 355–359.
-
B. C. Carlson (2006a)
Some reformulated properties of Jacobian elliptic functions.
J. Math. Anal. Appl. 323 (1), pp. 522–529.
-
B. C. Carlson (2006b)
Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric -functions.
Math. Comp. 75 (255), pp. 1309–1318.
-
B. C. Carlson (2008)
Power series for inverse Jacobian elliptic functions.
Math. Comp. 77 (263), pp. 1615–1621.
-
B. C. Carlson (2011)
Permutation symmetry for theta functions.
J. Math. Anal. Appl. 378 (1), pp. 42–48.
-
B. C. Carlson (1972b)
Intégrandes à deux formes quadratiques.
C. R. Acad. Sci. Paris Sér. A–B 274 (15 May, 1972, Sér. A), pp. 1458–1461 (French).
-
B. C. Carlson (1977b)
Special Functions of Applied Mathematics.
Academic Press, New York.
-
B. C. Carlson (1998)
Elliptic Integrals: Symmetry and Symbolic Integration.
In Tricomi’s Ideas and Contemporary Applied Mathematics
(Rome/Turin, 1997),
Atti dei Convegni Lincei, Vol. 147, pp. 161–181.
-
M. Carmignani and A. Tortorici Macaluso (1985)
Calcolo delle funzioni speciali , , , , alle alte precisioni.
Atti Accad. Sci. Lett. Arti Palermo Ser. (5) 2(1981/82) (1), pp. 7–25 (Italian).
-
L. D. Carr, C. W. Clark, and W. P. Reinhardt (2000)
Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity.
Phys. Rev. A 62 (063610), pp. 1–10.
-
H. S. Carslaw and J. C. Jaeger (1959)
Conduction of Heat in Solids.
2nd edition, Clarendon Press, Oxford.
-
H. S. Carslaw (1930)
Introduction to the Theory of Fourier’s Series and Integrals.
3rd edition, Macmillan, London.
-
J. R. Cash and R. V. M. Zahar (1994)
A Unified Approach to Recurrence Algorithms.
In Approximation and Computation (West Lafayette, IN, 1993), R. V. M. Zahar (Ed.),
International Series of Computational Mathematics, Vol. 119, pp. 97–120.
-
A. Cayley (1895)
An Elementary Treatise on Elliptic Functions.
George Bell and Sons, London.
-
A. Cayley (1961)
An Elementary Treatise on Elliptic Functions.
Dover Publications, New York (English).
-
R. Cazenave (1969)
Intégrales et Fonctions Elliptiques en Vue des Applications.
Préface de Henri Villat. Publications Scientifiques et
Techniques du Ministère de l’Air, No. 452, Centre de Documentation de l’Armement, Paris.
-
CEPHES (free C library)
-
H. H. Chan (1998)
On Ramanujan’s cubic transformation formula for .
Math. Proc. Cambridge Philos. Soc. 124 (2), pp. 193–204.
-
S. Chandrasekhar (1984)
The Mathematical Theory of Black Holes.
In General Relativity and Gravitation (Padova, 1983),
pp. 5–26.
-
F. Chapeau-Blondeau and A. Monir (2002)
Numerical evaluation of the Lambert function and application to generation of generalized Gaussian noise with exponent 1/2.
IEEE Trans. Signal Process. 50 (9), pp. 2160–2165.
-
C. J. Chapman (1999)
Caustics in cylindrical ducts.
Proc. Roy. Soc. London Ser. A 455, pp. 2529–2548.
-
B. W. Char (1980)
On Stieltjes’ continued fraction for the gamma function.
Math. Comp. 34 (150), pp. 547–551.
-
R. Chattamvelli and R. Shanmugam (1997)
Algorithm AS 310. Computing the non-central beta distribution function.
Appl. Statist. 46 (1), pp. 146–156.
-
M. A. Chaudhry, N. M. Temme, and E. J. M. Veling (1996)
Asymptotics and closed form of a generalized incomplete gamma function.
J. Comput. Appl. Math. 67 (2), pp. 371–379.
-
M. A. Chaudhry and S. M. Zubair (1994)
Generalized incomplete gamma functions with applications.
J. Comput. Appl. Math. 55 (1), pp. 99–124.
-
M. A. Chaudhry and S. M. Zubair (2001)
On a Class of Incomplete Gamma Functions with Applications.
Chapman & Hall/CRC, Boca Raton, FL.
-
T. W. Chaundy (1969)
Elementary Differential Equations.
Clarendon Press, Oxford.
-
A. D. Chave (1983)
Numerical integration of related Hankel transforms by quadrature and continued fraction expansion.
Geophysics 48 (12), pp. 1671–1686.
-
P. L. Chebyshev (1851)
Sur la fonction qui détermine la totalité des nombres premiers inférieurs à une limite donnée.
Mem. Ac. Sc. St. Pétersbourg 6, pp. 141–157.
-
M. Chellali (1988)
Accélération de calcul de nombres de Bernoulli.
J. Number Theory 28 (3), pp. 347–362 (French).
-
R. Chelluri, L. B. Richmond, and N. M. Temme (2000)
Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
-
J. Chen (1966)
On the representation of a large even integer as the sum of a prime and the product of at most two primes.
Kexue Tongbao (Foreign Lang. Ed.) 17, pp. 385–386.
-
L. Chen, M. E. H. Ismail, and P. Simeonov (1999)
Asymptotics of Racah coefficients and polynomials.
J. Phys. A 32 (3), pp. 537–553.
-
Y. Chen and M. E. H. Ismail (1998)
Asymptotics of the largest zeros of some orthogonal polynomials.
J. Phys. A 31 (25), pp. 5525–5544.
-
E. W. Cheney (1982)
Introduction to Approximation Theory.
2nd edition, Chelsea Publishing Co., New York.
-
I. Cherednik (1995)
Macdonald’s evaluation conjectures and difference Fourier transform.
Invent. Math. 122 (1), pp. 119–145.
-
T. M. Cherry (1948)
Expansions in terms of parabolic cylinder functions.
Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.
-
C. Chester, B. Friedman, and F. Ursell (1957)
An extension of the method of steepest descents.
Proc. Cambridge Philos. Soc. 53, pp. 599–611.
-
C. Chiccoli, S. Lorenzutta, and G. Maino (1987)
A numerical method for generalized exponential integrals.
Comput. Math. Appl. 14 (4), pp. 261–268.
-
C. Chiccoli, S. Lorenzutta, and G. Maino (1988)
On the evaluation of generalized exponential integrals .
J. Comput. Phys. 78 (2), pp. 278–287.
-
C. Chiccoli, S. Lorenzutta, and G. Maino (1990a)
An algorithm for exponential integrals of real order.
Computing 45 (3), pp. 269–276.
-
C. Chiccoli, S. Lorenzutta, and G. Maino (1990b)
On a Tricomi series representation for the generalized exponential integral.
Internat. J. Comput. Math. 31, pp. 257–262.
-
L. Chihara (1987)
On the zeros of the Askey-Wilson polynomials, with applications to coding theory.
SIAM J. Math. Anal. 18 (1), pp. 191–207.
-
T. S. Chihara (1978)
An Introduction to Orthogonal Polynomials.
Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York.
-
T. S. Chihara and M. E. H. Ismail (1993)
Extremal measures for a system of orthogonal polynomials.
Constr. Approx. 9, pp. 111–119.
-
Y. Chikuse (2003)
Statistics on Special Manifolds.
Lecture Notes in Statistics, Vol. 174, Springer-Verlag, New York.
-
R. C. Y. Chin and G. W. Hedstrom (1978)
A dispersion analysis for difference schemes: Tables of generalized Airy functions.
Math. Comp. 32 (144), pp. 1163–1170.
-
J. Choi and A. K. Rathie (2013)
An extension of a Kummer’s quadratic transformation formula with an application.
Proc. Jangjeon Math. Soc. 16 (2), pp. 229–235.
-
B. K. Choudhury (1995)
The Riemann zeta-function and its derivatives.
Proc. Roy. Soc. London Ser. A 450, pp. 477–499.
-
Y. Chow, L. Gatteschi, and R. Wong (1994)
A Bernstein-type inequality for the Jacobi polynomial.
Proc. Amer. Math. Soc. 121 (3), pp. 703–709.
-
N. B. Christensen (1990)
Optimized fast Hankel transform filters.
Geophysical Prospecting 38 (5), pp. 545–568.
-
J. S. Christiansen and M. E. H. Ismail (2006)
A moment problem and a family of integral evaluations.
Trans. Amer. Math. Soc. 358 (9), pp. 4071–4097.
-
J. A. Christley and I. J. Thompson (1994)
CRCWFN: Coupled real Coulomb wavefunctions.
Comput. Phys. Comm. 79 (1), pp. 143–155.
-
R. F. Christy and I. Duck (1961)
rays from an extranuclear direct capture process.
Nuclear Physics 24 (1), pp. 89–101.
-
G. Chrystal (1959a)
Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges.
6th edition, Vol. 1, Chelsea Publishing Co., New York.
-
G. Chrystal (1959b)
Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges.
6th edition, Vol. 2, Chelsea Publishing Co., New York.
-
D. V. Chudnovsky and G. V. Chudnovsky (1988)
Approximations and Complex Multiplication According to Ramanujan.
In Ramanujan Revisited (Urbana-Champaign, Ill., 1987), G. E. Andrews, R. A. Askey, B. C. Bernd, K. G. Ramanathan, and R. A. Rankin (Eds.),
pp. 375–472.
-
C. K. Chui (1988)
Multivariate Splines.
CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 54, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
-
A. Ciarkowski (1989)
Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point.
Proc. Roy. Soc. London Ser. A 426, pp. 273–286.
-
R. Cicchetti and A. Faraone (2004)
Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics.
IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
-
G. M. Cicuta and E. Montaldi (1975)
Remarks on the full asymptotic expansion of Feynman parametrized integrals.
Lett. Nuovo Cimento (2) 13 (8), pp. 310–312.
-
C. W. Clark (1979)
Coulomb phase shift.
American Journal of Physics 47 (8), pp. 683–684.
-
A. P. Clarke and W. Marwood (1984)
A compact mathematical function package.
Australian Computer Journal 16 (3), pp. 107–114.
-
F. Clarke (1989)
The universal von Staudt theorems.
Trans. Amer. Math. Soc. 315 (2), pp. 591–603.
-
P. A. Clarkson and M. D. Kruskal (1989)
New similarity reductions of the Boussinesq equation.
J. Math. Phys. 30 (10), pp. 2201–2213.
-
P. A. Clarkson and E. L. Mansfield (2003)
The second Painlevé equation, its hierarchy and associated special polynomials.
Nonlinearity 16 (3), pp. R1–R26.
-
P. A. Clarkson and J. B. McLeod (1988)
A connection formula for the second Painlevé transcendent.
Arch. Rational Mech. Anal. 103 (2), pp. 97–138.
-
P. A. Clarkson (1991)
Nonclassical Symmetry Reductions and Exact Solutions for Physically Significant Nonlinear Evolution Equations.
In Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids
(Edmonton, AB, 1990), W. Rozmus and J. A. Tuszynski (Eds.),
pp. 72–79.
-
P. A. Clarkson (2003a)
The third Painlevé equation and associated special polynomials.
J. Phys. A 36 (36), pp. 9507–9532.
-
P. A. Clarkson (2003b)
The fourth Painlevé equation and associated special polynomials.
J. Math. Phys. 44 (11), pp. 5350–5374.
-
P. A. Clarkson (2005)
Special polynomials associated with rational solutions of the fifth Painlevé equation.
J. Comput. Appl. Math. 178 (1-2), pp. 111–129.
-
P. A. Clarkson (2006)
Painlevé Equations—Nonlinear Special Functions: Computation and Application.
In Orthogonal Polynomials and Special Functions, F. Marcellàn and W. van Assche (Eds.),
Lecture Notes in Math., Vol. 1883, pp. 331–411.
-
T. Clausen (1828)
Über die Fälle, wenn die Reihe von der Form etc. ein Quadrat von der Form etc. hat.
J. Reine Angew. Math. 3, pp. 89–91.
-
D. S. Clemm (1969)
Algorithm 352: Characteristic values and associated solutions of Mathieu’s differential equation.
Comm. ACM 12 (7), pp. 399–407.
-
W. W. Clendenin (1966)
A method for numerical calculation of Fourier integrals.
Numer. Math. 8 (5), pp. 422–436.
-
C. W. Clenshaw and A. R. Curtis (1960)
A method for numerical integration on an automatic copmputer.
Numer. Math. 2 (4), pp. 197–205.
-
C. W. Clenshaw, D. W. Lozier, F. W. J. Olver, and P. R. Turner (1986)
Generalized exponential and logarithmic functions.
Comput. Math. Appl. Part B 12 (5-6), pp. 1091–1101.
-
C. W. Clenshaw, G. F. Miller, and M. Woodger (1962)
Algorithms for special functions. I.
Numer. Math. 4, pp. 403–419.
-
C. W. Clenshaw, F. W. J. Olver, and P. R. Turner (1989)
Level-Index Arithmetic: An Introductory Survey.
In Numerical Analysis and Parallel Processing (Lancaster, 1987), P. R. Turner (Ed.),
Lecture Notes in Math., Vol. 1397, pp. 95–168.
-
C. W. Clenshaw and F. W. J. Olver (1984)
Beyond floating point.
J. Assoc. Comput. Mach. 31 (2), pp. 319–328.
-
C. W. Clenshaw (1955)
A note on the summation of Chebyshev series.
Math. Tables Aids Comput. 9 (51), pp. 118–120.
-
C. W. Clenshaw (1957)
The numerical solution of linear differential equations in Chebyshev series.
Proc. Cambridge Philos. Soc. 53 (1), pp. 134–149.
-
C. W. Clenshaw (1962)
Chebyshev Series for Mathematical Functions.
National Physical Laboratory Mathematical Tables, Vol. 5.
Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
-
L. D. Cloutman (1989)
Numerical evaluation of the Fermi-Dirac integrals.
The Astrophysical Journal Supplement Series 71, pp. 677–699.
-
J. A. Cochran and J. N. Hoffspiegel (1970)
Numerical techniques for finding -zeros of Hankel functions.
Math. Comp. 24 (110), pp. 413–422.
-
J. A. Cochran (1963)
Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions.
IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.
-
J. A. Cochran (1964)
Remarks on the zeros of cross-product Bessel functions.
J. Soc. Indust. Appl. Math. 12 (3), pp. 580–587.
-
J. A. Cochran (1965)
The zeros of Hankel functions as functions of their order.
Numer. Math. 7 (3), pp. 238–250.
-
J. A. Cochran (1966a)
The analyticity of cross-product Bessel function zeros.
Proc. Cambridge Philos. Soc. 62, pp. 215–226.
-
J. A. Cochran (1966b)
The asymptotic nature of zeros of cross-product Bessel functions.
Quart. J. Mech. Appl. Math. 19 (4), pp. 511–522.
-
W. J. Cody, K. E. Hillstrom, and H. C. Thacher (1971)
Chebyshev approximations for the Riemann zeta function.
Math. Comp. 25 (115), pp. 537–547.
-
W. J. Cody and K. E. Hillstrom (1967)
Chebyshev approximations for the natural logarithm of the gamma function.
Math. Comp. 21 (98), pp. 198–203.
-
W. J. Cody and K. E. Hillstrom (1970)
Chebyshev approximations for the Coulomb phase shift.
Math. Comp. 24 (111), pp. 671–677.
-
W. J. Cody, K. A. Paciorek, and H. C. Thacher (1970)
Chebyshev approximations for Dawson’s integral.
Math. Comp. 24 (109), pp. 171–178.
-
W. J. Cody, A. J. Strecok, and H. C. Thacher (1973)
Chebyshev approximations for the psi function.
Math. Comp. 27 (121), pp. 123–127.
-
W. J. Cody and H. C. Thacher (1968)
Rational Chebyshev approximations for the exponential integral .
Math. Comp. 22 (103), pp. 641–649.
-
W. J. Cody and H. C. Thacher (1969)
Chebyshev approximations for the exponential integral .
Math. Comp. 23 (106), pp. 289–303.
-
W. J. Cody and W. Waite (1980)
Software Manual for the Elementary Functions.
Prentice-Hall, Englewood Cliffs.
-
W. J. Cody (1965a)
Chebyshev approximations for the complete elliptic integrals and .
Math. Comp. 19 (89), pp. 105–112.
-
W. J. Cody (1965b)
Chebyshev polynomial expansions of complete elliptic integrals.
Math. Comp. 19 (90), pp. 249–259.
-
W. J. Cody (1968)
Chebyshev approximations for the Fresnel integrals.
Math. Comp. 22 (102), pp. 450–453.
-
W. J. Cody (1969)
Rational Chebyshev approximations for the error function.
Math. Comp. 23 (107), pp. 631–637.
-
W. J. Cody (1970)
A survey of practical rational and polynomial approximation of functions.
SIAM Rev. 12 (3), pp. 400–423.
-
W. J. Cody (1983)
Algorithm 597: Sequence of modified Bessel functions of the first kind.
ACM Trans. Math. Software 9 (2), pp. 242–245.
-
W. J. Cody (1991)
Performance evaluation of programs related to the real gamma function.
ACM Trans. Math. Software 17 (1), pp. 46–54.
-
W. J. Cody (1993a)
Algorithm 714: CELEFUNT – A portable test package for complex elementary functions.
ACM Trans. Math. Software 19 (1), pp. 1–21.
-
W. J. Cody (1993b)
Algorithm 715: SPECFUN – A portable FORTRAN package of special function routines and test drivers.
ACM Trans. Math. Software 19 (1), pp. 22–32.
-
M. W. Coffey (2008)
On some series representations of the Hurwitz zeta function.
J. Comput. Appl. Math. 216 (1), pp. 297–305.
-
M. W. Coffey (2009)
An efficient algorithm for the Hurwitz zeta and related functions.
J. Comput. Appl. Math. 225 (2), pp. 338–346.
-
H. Cohen (1993)
A Course in Computational Algebraic Number Theory.
Springer-Verlag, Berlin-New York.
-
H. S. Cohl (2010)
Derivatives with respect to the degree and order of associated Legendre functions for using modified Bessel functions.
Integral Transforms Spec. Funct. 21 (7-8), pp. 581–588.
-
H. S. Cohl (2011)
On parameter differentiation for integral representations of associated Legendre functions.
SIGMA Symmetry Integrability Geom. Methods Appl. 7, pp. Paper 050, 16.
-
H. S. Cohl (2013a)
Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems.
SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.
-
H. S. Cohl (2013b)
On a generalization of the generating function for Gegenbauer polynomials.
Integral Transforms Spec. Funct. 24 (10), pp. 807–816.
-
J. P. Coleman and A. J. Monaghan (1983)
Chebyshev expansions for the Bessel function in the complex plane.
Math. Comp. 40 (161), pp. 343–366.
-
J. P. Coleman (1980)
A Fortran subroutine for the Bessel function of order to .
Comput. Phys. Comm. 21 (1), pp. 109–118.
-
J. P. Coleman (1987)
Polynomial approximations in the complex plane.
J. Comput. Appl. Math. 18 (2), pp. 193–211.
-
L. Collatz (1960)
The Numerical Treatment of Differential Equations.
3rd edition, Die Grundlehren der Mathematischen Wissenschaften, Vol. 60, Springer, Berlin.
-
M. Colman, A. Cuyt, and J. Van Deun (2011)
Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
-
D. Colton and R. Kress (1998)
Inverse Acoustic and Electromagnetic Scattering Theory.
2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.
-
Combinatorial Object Server (website)
Department of Computer Science, University of Victoria, Canada.
-
L. Comtet (1974)
Advanced Combinatorics: The Art of Finite and Infinite Expansions.
enlarged edition, D. Reidel Publishing Co., Dordrecht.
-
S. Conde and S. L. Kalla (1979)
The -zeros of .
Math. Comp. 33 (145), pp. 423–426.
-
S. Conde and S. L. Kalla (1981)
On zeros of the hypergeometric function.
Serdica 7 (3), pp. 243–249.
-
E. U. Condon and G. H. Shortley (1935)
The Theory of Atomic Spectra.
Cambridge University Press, Cambridge.
-
W. C. Connett, C. Markett, and A. L. Schwartz (1993)
Product formulas and convolutions for angular and radial spheroidal wave functions.
Trans. Amer. Math. Soc. 338 (2), pp. 695–710.
-
J. N. L. Connor, P. R. Curtis, and D. Farrelly (1983)
A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives.
Molecular Phys. 48 (6), pp. 1305–1330.
-
J. N. L. Connor and P. R. Curtis (1982)
A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: Application to Pearcey’s integral and its derivatives.
J. Phys. A 15 (4), pp. 1179–1190.
-
J. N. L. Connor and D. Farrelly (1981)
Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey’s integral and its derivatives.
Chem. Phys. Lett. 81 (2), pp. 306–310.
-
J. N. L. Connor and D. C. Mackay (1979)
Calculation of angular distributions in complex angular momentum theories of elastic scattering.
Molecular Physics 37 (6), pp. 1703–1712.
-
J. N. L. Connor (1973)
Evaluation of multidimensional canonical integrals in semiclassical collision theory.
Molecular Phys. 26 (6), pp. 1371–1377.
-
J. N. L. Connor (1974)
Semiclassical theory of molecular collisions: Many nearly coincident classical trajectories.
Molecular Phys. 27 (4), pp. 853–866.
-
J. N. L. Connor (1976)
Catastrophes and molecular collisions.
Molecular Phys. 31 (1), pp. 33–55.
-
A. G. Constantine (1963)
Some non-central distribution problems in multivariate analysis.
Ann. Math. Statist. 34 (4), pp. 1270–1285.
-
E. D. Constantinides and R. J. Marhefka (1993)
Efficient and accurate computation of the incomplete Airy functions.
Radio Science 28 (4), pp. 441–457.
-
J. W. Cooley and J. W. Tukey (1965)
An algorithm for the machine calculation of complex Fourier series.
Math. Comp. 19 (90), pp. 297–301.
-
R. Cools (2003)
An encyclopaedia of cubature formulas.
J. Complexity 19 (3), pp. 445–453.
-
F. Cooper, A. Khare, and A. Saxena (2006)
Exact elliptic compactons in generalized Korteweg-de Vries equations.
Complexity 11 (6), pp. 30–34.
-
M. D. Cooper, R. H. Jeppesen, and M. B. Johnson (1979)
Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
-
R. B. Cooper (1981)
Introduction to Queueing Theory.
2nd edition, North-Holland Publishing Co., New York.
-
E. T. Copson (1933)
An approximation connected with .
Proc. Edinburgh Math. Soc. (2) 3, pp. 201–206.
-
E. T. Copson (1935)
An Introduction to the Theory of Functions of a Complex Variable.
Oxford University Press, Oxford.
-
E. T. Copson (1963)
On the asymptotic expansion of Airy’s integral.
Proc. Glasgow Math. Assoc. 6, pp. 113–115.
-
E. T. Copson (1965)
Asymptotic Expansions.
Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, New York.
-
R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth (1996)
On the Lambert function.
Adv. Comput. Math. 5 (4), pp. 329–359.
-
R. M. Corless, D. J. Jeffrey, and H. Rasmussen (1992)
Numerical evaluation of Airy functions with complex arguments.
J. Comput. Phys. 99 (1), pp. 106–114.
-
G. Cornell, J. H. Silverman, and G. Stevens (Eds.) (1997)
Modular Forms and Fermat’s Last Theorem.
Springer-Verlag, New York.
-
H. Cornille and A. Martin (1972)
Constraints on the phase of scattering amplitudes due to positivity.
Nuclear Phys. B 49, pp. 413–440.
-
H. Cornille and A. Martin (1974)
Constraints on the phases of helicity amplitudes due to positivity.
Nuclear Phys. B 77, pp. 141–162.
-
P. Cornille (1972)
Computation of Hankel transforms.
SIAM Rev. 14 (2), pp. 278–285.
-
M. S. Corrington (1961)
Applications of the complex exponential integral.
Math. Comp. 15 (73), pp. 1–6.
-
C. M. Cosgrove (2006)
Chazy’s second-degree Painlevé equations.
J. Phys. A 39 (39), pp. 11955–11971.
-
O. Costin (1999)
Correlation between pole location and asymptotic behavior for Painlevé I solutions.
Comm. Pure Appl. Math. 52 (4), pp. 461–478.
-
CoStLy (free C-XSC library)
-
R. Courant and D. Hilbert (1953)
Methods of mathematical physics. Vol. I.
Interscience Publishers, Inc., New York, N.Y..
-
D. A. Cox (1984)
The arithmetic-geometric mean of Gauss.
Enseign. Math. (2) 30 (3-4), pp. 275–330.
-
D. A. Cox (1985)
Gauss and the arithmetic-geometric mean.
Notices Amer. Math. Soc. 32 (2), pp. 147–151.
-
R. E. Crandall (1996)
Topics in Advanced Scientific Computation.
TELOS/Springer-Verlag, New York.
-
R. Crandall and C. Pomerance (2005)
Prime Numbers: A Computational Perspective.
2nd edition, Springer-Verlag, New York.
-
J. E. Cremona (1997)
Algorithms for Modular Elliptic Curves.
2nd edition, Cambridge University Press, Cambridge.
-
J. Crisóstomo, S. Lepe, and J. Saavedra (2004)
Quasinormal modes of the extremal BTZ black hole.
Classical Quantum Gravity 21 (12), pp. 2801–2809.
-
D. C. Cronemeyer (1991)
Demagnetization factors for general ellipsoids.
J. Appl. Phys. 70 (6), pp. 2911–2914.
-
B. Crstici and Gh. Tudor (1975)
Compléments au traité de D. S. Mitrinović. VII. Sur une inégalité de D. S. Mitrinović.
Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (498-541), pp. 153–154.
-
A. Cruz, J. Esparza, and J. Sesma (1991)
Zeros of the Hankel function of real order out of the principal Riemann sheet.
J. Comput. Appl. Math. 37 (1-3), pp. 89–99.
-
A. Cruz and J. Sesma (1982)
Zeros of the Hankel function of real order and of its derivative.
Math. Comp. 39 (160), pp. 639–645.
-
A. Csótó and G. M. Hale (1997)
-matrix and -matrix determination of the low-energy and resonance parameters.
Phys. Rev. C 55 (1), pp. 536–539.
-
Cunningham Project (website)
-
S. W. Cunningham (1969)
Algorithm AS 24: From normal integral to deviate.
Appl. Statist. 18 (3), pp. 290–293.
-
A. R. Curtis (1964a)
Coulomb Wave Functions.
Roy. Soc. Math. Tables, Vol. 11, Cambridge University Press, Cambridge.
-
A. R. Curtis (1964b)
Tables of Jacobian Elliptic Functions Whose Arguments are Rational Fractions of the Quarter Period.
National Physical Laboratory Mathematical Tables, Vol. 7, Her Majesty’s Stationery Office, London.
-
A. Cuyt, V. Petersen, B. Verdonk, H. Waadeland, W. B. Jones, and C. Bonan-Hamada (2007)
Handbook of Continued Fractions for Special Functions.
Kluwer Academic Publishers Group, Dordrecht.
-
A. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland, and W. B. Jones (2008)
Handbook of Continued Fractions for Special Functions.
Springer, New York.
-
D. Cvijović and J. Klinowski (1994)
On the integration of incomplete elliptic integrals.
Proc. Roy. Soc. London Ser. A 444, pp. 525–532.
-
D. Cvijović and J. Klinowski (1999)
Integrals involving complete elliptic integrals.
J. Comput. Appl. Math. 106 (1), pp. 169–175.