-
J. Abad and J. Sesma (1995)
Computation of the regular confluent hypergeometric function,
The Mathematica Journal 5 (4), pp. 74–76.
-
A. S. Abdullaev (1985)
Asymptotics of solutions of the generalized sine-Gordon equation, the third Painlevé equation and the d’Alembert equation,
Dokl. Akad. Nauk SSSR 280 (2), pp. 265–268 (Russian).
-
R. W. Abernathy and R. P. Smith (1993)
Algorithm 724: Program to calculate F-percentiles,
ACM Trans. Math. Software 19 (4), pp. 481–483.
-
M. J. Ablowitz and P. A. Clarkson (1991)
Solitons, Nonlinear Evolution Equations and Inverse Scattering,
London Mathematical Society Lecture Note Series, Vol. 149, Cambridge University Press, Cambridge.
-
M. J. Ablowitz and H. Segur (1977)
Exact linearization of a Painlevé transcendent,
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
-
M. J. Ablowitz and H. Segur (1981)
Solitons and the Inverse Scattering Transform,
SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
-
A. Abramov (1960)
Tables of for Complex Argument,
Pergamon Press, New York.
-
M. Abramowitz and P. Rabinowitz (1954)
Evaluation of Coulomb wave functions along the transition line,
Physical Rev. (2) 96, pp. 77–79.
-
M. Abramowitz and I. A. Stegun (Eds.) (1964)
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,
National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
-
M. Abramowitz (1949)
Asymptotic expansions of spheroidal wave functions,
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
-
M. Abramowitz (1954)
Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions,
J. Math. Physics 33, pp. 111–116.
-
J. Achenbach (1986)
Numerik: Implementierung von Zylinderfunktionen,
Elektrotechnik, Friedr. Vieweg & Sohn, Braunschweig-Wiesbaden.
-
F. S. Acton (1974)
Recurrence relations for the Fresnel integral and similar integrals,
Comm. ACM 17 (8), pp. 480–481.
-
V. S. Adamchik and H. M. Srivastava (1998)
Some series of the zeta and related functions,
Analysis (Munich) 18 (2), pp. 131–144.
-
V. S. Adamchik (1998)
Polygamma functions of negative order,
J. Comput. Appl. Math. 100 (2), pp. 191–199.
-
A. G. Adams (1969)
Algorithm 39: Areas under the normal curve,
The Computer Journal 12 (2), pp. 197–198.
-
J. C. Adams and P. N. Swarztrauber (1997)
SPHEREPACK 2.0: A Model Development Facility,
NCAR Technical Note
Technical Report TN-436-STR, National Center for Atmospheric Research.
-
A. Adelberg (1992)
On the degrees of irreducible factors of higher order Bernoulli polynomials,
Acta Arith. 62 (4), pp. 329–342.
-
A. Adelberg (1996)
Congruences of -adic integer order Bernoulli numbers,
J. Number Theory 59 (2), pp. 374–388.
-
C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson (1985)
Chapter 16 of Ramanujan’s second notebook: Theta-functions and -series,
Mem. Amer. Math. Soc. 53 (315), pp. v+85.
-
C. L. Adler, J. A. Lock, B. R. Stone and C. J. Garcia (1997)
High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder,
J. Opt. Soc. Amer. A 14 (6), pp. 1305–1315.
-
V. È. Adler (1994)
Nonlinear chains and Painlevé equations,
Phys. D 73 (4), pp. 335–351.
-
P. Adrian (1959)
Die Bezeichnungsweise der Bernoullischen Zahlen,
Mitt. Verein. Schweiz. Versicherungsmath. 59, pp. 199–206 (German).
-
M. M. Agrest, S. I. Labakhua, M. M. Rikenglaz and Ts. Sh. Chachibaya (1982)
Tablitsy funktsii Struve i integralov ot nikh,
“Nauka”, Moscow (Russian).
-
M. M. Agrest and M. S. Maksimov (1971)
Theory of Incomplete Cylindrical Functions and Their Applications,
Springer-Verlag, Berlin.
-
L. V. Ahlfors (1966)
Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable,
2nd edition, McGraw-Hill Book Co., New York.
-
A. R. Ahmadi and S. E. Widnall (1985)
Unsteady lifting-line theory as a singular-perturbation problem,
J. Fluid Mech 153, pp. 59–81.
-
S. Ahmed and M. E. Muldoon (1980)
On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations,
Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.
-
S-H. Ahn, H. Lee and H. M. Lee (2001)
Ly line formation in starbursting galaxies. I. Moderately thick, dustless, and static H i media,
Astrophysical J. 554, pp. 604–614.
-
H. Airault, H. P. McKean and J. Moser (1977)
Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem,
Comm. Pure Appl. Math. 30 (1), pp. 95–148.
-
H. Airault (1979)
Rational solutions of Painlevé equations,
Stud. Appl. Math. 61 (1), pp. 31–53.
-
G. B. Airy (1838)
On the intensity of light in the neighbourhood of a caustic,
Trans. Camb. Phil. Soc. 6, pp. 379–402.
-
G. B. Airy (1849)
Supplement to a paper “On the intensity of light in the neighbourhood of a caustic”,
Trans. Camb. Phil. Soc. 8, pp. 595–599.
-
N. I. Akhiezer (1988)
Lectures on Integral Transforms,
Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.
-
N. I. Akhiezer (1990)
Elements of the Theory of Elliptic Functions,
Translations of Mathematical Monographs, Vol. 79, American Mathematical Society, Providence, RI.
-
S. V. Aksenov, M. A. Savageau, U. D. Jentschura, J. Becher, G. Soff and P. J. Mohr (2003)
Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics,
Comput. Phys. Comm. 150 (1), pp. 1–20.
-
A. M. Al-Rashed and N. Zaheer (1985)
Zeros of Stieltjes and Van Vleck polynomials and applications,
J. Math. Anal. Appl. 110 (2), pp. 327–339.
-
W. A. Al-Salam and L. Carlitz (1959)
Some determinants of Bernoulli, Euler and related numbers,
Portugal. Math. 18, pp. 91–99.
-
W. A. Al-Salam and L. Carlitz (1965)
Some orthogonal -polynomials,
Math. Nachr. 30, pp. 47–61.
-
W. A. Al-Salam and M. E. H. Ismail (1994)
A -beta integral on the unit circle and some biorthogonal rational functions,
Proc. Amer. Math. Soc. 121 (2), pp. 553–561.
-
M. Alam (1979)
Zeros of Stieltjes and Van Vleck polynomials,
Trans. Amer. Math. Soc. 252, pp. 197–204.
-
D. W. Albrecht, E. L. Mansfield and A. E. Milne (1996)
Algorithms for special integrals of ordinary differential equations,
J. Phys. A 29 (5), pp. 973–991.
-
J. R. Albright and E. P. Gavathas (1986)
Integrals involving Airy functions,
J. Phys. A 19 (13), pp. 2663–2665.
-
J. R. Albright (1977)
Integrals of products of Airy functions,
J. Phys. A 10 (4), pp. 485–490.
-
K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther (1956)
Study of nuclear structure by electromagnetic excitation with accelerated ions,
Rev. Mod. Phys. 28, pp. 432–542.
-
G. Alefeld and J. Herzberger (1983)
Introduction to Interval Computations,
Computer Science and Applied Mathematics, Academic Press Inc., New York.
-
W. R. Alford, A. Granville and C. Pomerance (1994)
There are infinitely many Carmichael numbers,
Ann. of Math. (2) 139 (3), pp. 703–722.
-
F. Alhargan and S. Judah (1992)
Frequency response characteristics of the multiport planar elliptic patch,
IEEE Trans. Microwave Theory Tech. 40 (8), pp. 1726–1730.
-
F. Alhargan and S. Judah (1995)
A general mode theory for the elliptic disk microstrip antenna,
IEEE Trans. Antennas and Propagation 43 (6), pp. 560–568.
-
F. A. Alhargan (2000)
Algorithm 804: Subroutines for the computation of Mathieu functions of integer orders,
ACM Trans. Math. Software 26 (3), pp. 408–414.
-
G. Allasia and R. Besenghi (1987a)
Numerical computation of Tricomi’s psi function by the trapezoidal rule,
Computing 39 (3), pp. 271–279.
-
G. Allasia and R. Besenghi (1991)
Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule,
Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.
-
G. Allasia and R. Besenghi (1987b)
Numerical calculation of incomplete gamma functions by the trapezoidal rule,
Numer. Math. 50 (4), pp. 419–428.
-
G. Allasia and R. Besenghi (1989)
Numerical Calculation of the Riemann Zeta Function and Generalizations by Means of the Trapezoidal Rule,
in Numerical and Applied Mathematics, Part II (Paris, 1988),
IMACS Ann. Comput. Appl. Math., Vol. 1, pp. 467–472.
-
G. Almkvist and B. Berndt (1988)
Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, , and the Ladies Diary,
Amer. Math. Monthly 95 (7), pp. 585–608.
-
Z. Altaç (1996)
Integrals involving Bickley and Bessel functions in radiative transfer, and generalized exponential integral functions,
J. Heat Transfer 118 (3), pp. 789–792.
-
H. H. Aly, H. J. W. Müller-Kirsten and N. Vahedi-Faridi (1975)
Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions,
J. Mathematical Phys. 16, pp. 961–970.
-
H. Alzer and S. Qiu (2004)
Monotonicity theorems and inequalities for the complete elliptic integrals,
J. Comput. Appl. Math. 172 (2), pp. 289–312.
-
H. Alzer (1997a)
A harmonic mean inequality for the gamma function,
J. Comput. Appl. Math. 87 (2), pp. 195–198.
-
H. Alzer (1997b)
On some inequalities for the incomplete gamma function,
Math. Comp. 66 (218), pp. 771–778.
-
H. Alzer (2000)
Sharp bounds for the Bernoulli numbers,
Arch. Math. (Basel) 74 (3), pp. 207–211.
-
H. Alzer (2008)
Gamma function inequalities,
Numer. Algorithms 49 (1-4), pp. 53–84.
-
D. E. Amos, S. L. Daniel and M. K. Weston (1977)
ACM Trans. Math. Software 3 (1), pp. 93–95.
-
D. E. Amos (1974)
Computation of modified Bessel functions and their ratios,
Math. Comp. 28 (125), pp. 239–251.
-
D. E. Amos (1983a)
Algorithm 609. A portable FORTRAN subroutine for the Bickley functions ,
ACM Trans. Math. Software 9 (4), pp. 480–493.
-
D. E. Amos (1983b)
Algorithm 610. A portable FORTRAN subroutine for derivatives of the psi function,
ACM Trans. Math. Software 9 (4), pp. 494–502.
-
D. E. Amos (1983c)
Uniform asymptotic expansions for exponential integrals and Bickley functions ,
ACM Trans. Math. Software 9 (4), pp. 467–479.
-
D. E. Amos (1985)
A subroutine package for Bessel functions of a complex argument and nonnegative order,
Technical Report
Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.
-
D. E. Amos (1986)
Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order,
ACM Trans. Math. Software 12 (3), pp. 265–273.
-
D. E. Amos (1980a)
Algorithm 556: Exponential integrals,
ACM Trans. Math. Software 6 (3), pp. 420–428.
-
D. E. Amos (1980b)
Computation of exponential integrals,
ACM Trans. Math. Software 6 (3), pp. 365–377.
-
D. E. Amos (1989)
Repeated integrals and derivatives of Bessel functions,
SIAM J. Math. Anal. 20 (1), pp. 169–175.
-
D. E. Amos (1990)
Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument,
ACM Trans. Math. Software 16 (2), pp. 178–182.
-
G. D. Anderson, S.-L. Qiu, M. K. Vamanamurthy and M. Vuorinen (2000)
Generalized elliptic integrals and modular equations,
Pacific J. Math. 192 (1), pp. 1–37.
-
G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen (1990)
Functional inequalities for complete elliptic integrals and their ratios,
SIAM J. Math. Anal. 21 (2), pp. 536–549.
-
G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen (1992a)
Functional inequalities for hypergeometric functions and complete elliptic integrals,
SIAM J. Math. Anal. 23 (2), pp. 512–524.
-
G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen (1992b)
Hypergeometric Functions and Elliptic Integrals,
in Current Topics in Analytic Function Theory,
(S. Owa Ed.), pp. 48–85.
-
G. D. Anderson and M. K. Vamanamurthy (1985)
Inequalities for elliptic integrals,
Publ. Inst. Math. (Beograd) (N.S.) 37(51), pp. 61–63.
-
G. D. Anderson, M. K. Vamanamurthy and M. K. Vuorinen (1997)
Conformal Invariants, Inequalities, and Quasiconformal Maps,
John Wiley & Sons Inc., New York.