Bibliography P
-
K. A. Paciorek (1970)
Algorithm 385: Exponential integral .
Comm. ACM 13 (7), pp. 446–447.
-
V. I. Pagurova (1961)
Tables of the Exponential Integral .
Pergamon Press, New York.
-
V. I. Pagurova (1963)
Tablitsy nepolnoi gamma-funktsii.
Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).
-
V. I. Pagurova (1965)
An asymptotic formula for the incomplete gamma function.
Ž. Vyčisl. Mat. i Mat. Fiz. 5, pp. 118–121 (Russian).
-
P. Painlevé (1906)
Sur les équations différentielles du second ordre à points critiques fixès.
C.R. Acad. Sc. Paris 143, pp. 1111–1117.
-
E. Pairman (1919)
Tables of Digamma and Trigamma Functions.
In Tracts for Computers, No. 1, K. Pearson (Ed.),
-
B. V. Paltsev (1999)
On two-sided estimates, uniform with respect to the real argument and index, for modified Bessel functions.
Mat. Zametki 65 (5), pp. 681–692 (Russian).
-
T. Pálmai and B. Apagyi (2011)
Interlacing of positive real zeros of Bessel functions.
J. Math. Anal. Appl. 375 (1), pp. 320–322.
-
D. J. Panow (1955)
Formelsammlung zur numerischen Behandlung partieller Differentialgleichungen nach dem Differenzenverfahren.
Akademie-Verlag, Berlin (German).
-
A. Papoulis (1977)
Signal Analysis.
McGraw-Hill, New York.
-
PARI-GP (free interactive system and C library)
-
R. B. Paris and S. Cang (1997)
An asymptotic representation for .
Methods Appl. Anal. 4 (4), pp. 449–470.
-
R. B. Paris and D. Kaminski (2001)
Asymptotics and Mellin-Barnes Integrals.
Cambridge University Press, Cambridge.
-
R. B. Paris and W. N.-C. Sy (1983)
Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability.
Phys. Fluids 26 (10), pp. 2966–2975.
-
R. B. Paris and A. D. Wood (1995)
Stokes phenomenon demystified.
Bull. Inst. Math. Appl. 31 (1-2), pp. 21–28.
-
R. B. Paris (1984)
An inequality for the Bessel function .
SIAM J. Math. Anal. 15 (1), pp. 203–205.
-
R. B. Paris (1991)
The asymptotic behaviour of Pearcey’s integral for complex variables.
Proc. Roy. Soc. London Ser. A 432 (1886), pp. 391–426.
-
R. B. Paris (1992a)
Smoothing of the Stokes phenomenon for high-order differential equations.
Proc. Roy. Soc. London Ser. A 436, pp. 165–186.
-
R. B. Paris (1992b)
Smoothing of the Stokes phenomenon using Mellin-Barnes integrals.
J. Comput. Appl. Math. 41 (1-2), pp. 117–133.
-
R. B. Paris (2001a)
On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables.
Proc. Roy. Soc. London Ser. A 457 (2016), pp. 2835–2853.
-
R. B. Paris (2001b)
On the use of Hadamard expansions in hyperasymptotic evaluation. II. Complex variables.
Proc. Roy. Soc. London Ser. A 457, pp. 2855–2869.
-
R. B. Paris (2002a)
Error bounds for the uniform asymptotic expansion of the incomplete gamma function.
J. Comput. Appl. Math. 147 (1), pp. 215–231.
-
R. B. Paris (2002b)
A uniform asymptotic expansion for the incomplete gamma function.
J. Comput. Appl. Math. 148 (2), pp. 323–339.
-
R. B. Paris (2002c)
Exponential asymptotics of the Mittag-Leffler function.
Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
-
R. B. Paris (2003)
The asymptotic expansion of a generalised incomplete gamma function.
J. Comput. Appl. Math. 151 (2), pp. 297–306.
-
R. B. Paris (2004)
Exactification of the method of steepest descents: The Bessel functions of large order and argument.
Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
-
R. B. Paris (2005a)
A Kummer-type transformation for a hypergeometric function.
J. Comput. Appl. Math. 173 (2), pp. 379–382.
-
R. B. Paris (2005b)
The Stokes phenomenon associated with the Hurwitz zeta function .
Proc. Roy. Soc. London Ser. A 461, pp. 297–304.
-
R. B. Paris (2013)
Exponentially small expansions of the confluent hypergeometric functions.
Appl. Math. Sci. (Ruse) 7 (133-136), pp. 6601–6609.
-
G. Parisi (1988)
Statistical Field Theory.
Addison-Wesley, Reading, MA.
-
A. M. Parkhurst and A. T. James (1974)
Zonal Polynomials of Order Through .
In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.),
Vol. 2, pp. 199–388.
-
J. B. Parkinson (1969)
Optical properties of layer antiferromagnets with structure.
J. Phys. C: Solid State Physics 2 (11), pp. 2012–2021.
-
R. Parnes (1972)
Complex zeros of the modified Bessel function .
Math. Comp. 26 (120), pp. 949–953.
-
P. I. Pastro (1985)
Orthogonal polynomials and some -beta integrals of Ramanujan.
J. Math. Anal. Appl. 112 (2), pp. 517–540.
-
S. Paszkowski (1988)
Evaluation of Fermi-Dirac Integral.
In Nonlinear Numerical Methods and Rational Approximation
(Wilrijk, 1987), A. Cuyt (Ed.),
Mathematics and Its Applications, Vol. 43, pp. 435–444.
-
S. Paszkowski (1991)
Evaluation of the Fermi-Dirac integral of half-integer order.
Zastos. Mat. 21 (2), pp. 289–301.
-
J. K. Patel and C. B. Read (1982)
Handbook of the Normal Distribution.
Statistics: Textbooks and Monographs, Vol. 40, Marcel Dekker Inc., New York.
-
J. Patera and P. Winternitz (1973)
A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys. 14 (8), pp. 1130–1139.
-
A. R. Paterson (1983)
A First Course in Fluid Dynamics.
Cambridge University Press, Cambridge.
-
F. A. Paxton and J. E. Rollin (1959)
Tables of the Incomplete Elliptic Integrals of the First and Third Kind.
Technical report
Curtiss-Wright Corp., Research Division, Quehanna, PA.
-
T. Pearcey (1946)
The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic.
Philos. Mag. (7) 37, pp. 311–317.
-
K. Pearson (Ed.) (1965)
Tables of the Incomplete -function.
Biometrika Office, Cambridge University Press, Cambridge.
-
K. Pearson (Ed.) (1968)
Tables of the Incomplete Beta-function.
2nd edition, Published for the Biometrika Trustees at the Cambridge
University Press, Cambridge.
-
T. G. Pedersen (2003)
Variational approach to excitons in carbon nanotubes.
Phys. Rev. B 67 (7), pp. (073401–1)–(073401–4).
-
W. F. Perger, A. Bhalla, and M. Nardin (1993)
A numerical evaluator for the generalized hypergeometric series.
Comput. Phys. Comm. 77 (2), pp. 249–254.
-
M. D. Perlman and I. Olkin (1980)
Unbiasedness of invariant tests for MANOVA and other multivariate problems.
Ann. Statist. 8 (6), pp. 1326–1341.
-
G. Petiau (1955)
La Théorie des Fonctions de Bessel Exposée en vue de ses Applications à la Physique Mathématique.
Centre National de la Recherche Scientifique, Paris (French).
-
M. S. Petković and L. D. Petković (1998)
Complex Interval Arithmetic and its Applications.
Mathematical Research, Vol. 105, Wiley-VCH Verlag Berlin GmbH, Berlin.
-
M. Petkovšek, H. S. Wilf, and D. Zeilberger (1996)
.
A K Peters Ltd., Wellesley, MA.
-
E. Petropoulou (2000)
Bounds for ratios of modified Bessel functions.
Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
-
H. N. Phien (1988)
A Fortran routine for the computation of gamma percentiles.
Adv. Eng. Software 10 (3), pp. 159–164.
-
H. N. Phien (1990)
A note on the computation of the incomplete beta function.
Adv. Eng. Software 12 (1), pp. 39–44.
-
P. C. B. Phillips (1986)
The exact distribution of the Wald statistic.
Econometrica 54 (4), pp. 881–895.
-
B. Pichon (1989)
Numerical calculation of the generalized Fermi-Dirac integrals.
Comput. Phys. Comm. 55 (2), pp. 127–136.
-
R. Piessens (1982)
Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
-
R. Piessens (1984a)
Chebyshev series approximations for the zeros of the Bessel functions.
J. Comput. Phys. 53 (1), pp. 188–192.
-
R. Piessens (1984b)
The computation of Bessel functions on a small computer.
Comput. Math. Appl. 10 (2), pp. 161–166.
-
R. Piessens (1990)
On the computation of zeros and turning points of Bessel functions.
Bull. Soc. Math. Grèce (N.S.) 31, pp. 117–122.
-
R. Piessens and S. Ahmed (1986)
Approximation for the turning points of Bessel functions.
J. Comput. Phys. 64 (1), pp. 253–257.
-
R. Piessens and M. Branders (1972)
Chebyshev polynomial expansions of the Riemann zeta function.
Math. Comp. 26 (120), pp. G1–G5.
-
R. Piessens and M. Branders (1983)
Modified Clenshaw-Curtis method for the computation of Bessel function integrals.
BIT 23 (3), pp. 370–381.
-
R. Piessens and M. Branders (1984)
Algorithm 28. Algorithm for the computation of Bessel function integrals.
J. Comput. Appl. Math. 11 (1), pp. 119–137.
-
R. Piessens and M. Branders (1985)
A survey of numerical methods for the computation of Bessel function integrals.
Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 249–265.
-
A. Pinkus and S. Zafrany (1997)
Fourier Series and Integral Transforms.
Cambridge University Press, Cambridge.
-
G. Pittaluga and L. Sacripante (1991)
Inequalities for the zeros of the Airy functions.
SIAM J. Math. Anal. 22 (1), pp. 260–267.
-
S. Pokorski (1987)
Gauge Field Theories.
Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
-
J. Polchinski (1998)
String Theory: An Introduction to the Bosonic String, Vol. I.
Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
-
G. Pólya and R. C. Read (1987)
Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds.
Springer-Verlag, New York.
-
G. Pólya, R. E. Tarjan, and D. R. Woods (1983)
Notes on Introductory Combinatorics.
Progress in Computer Science, Vol. 4, Birkhäuser Boston Inc., Boston, MA.
-
G. Pólya (1937)
Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen.
Acta Mathematica 68, pp. 145–254.
-
G. Pólya (1949)
Remarks on computing the probability integral in one and two dimensions.
In Proceedings of the Berkeley Symposium on Mathematical
Statistics and Probability, 1945, 1946,
pp. 63–78.
-
G. P. M. Poppe and C. M. J. Wijers (1990)
Algorithm 680: Evaluation of the complex error function.
ACM Trans. Math. Software 16 (1), pp. 47.
-
A. Poquérusse and S. Alexiou (1999)
Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations.
J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.
-
S. Porubský (1998)
Voronoi type congruences for Bernoulli numbers.
In Voronoi’s Impact on Modern Science. Book I, P. Engel and H. Syta (Eds.),
-
T. Poston and I. Stewart (1978)
Catastrophe Theory and its Applications.
Pitman, London.
-
J. L. Powell (1947)
Recurrence formulas for Coulomb wave functions.
Physical Rev. (2) 72 (7), pp. 626–627.
-
M. J. D. Powell (1967)
On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria.
Comput. J. 9 (4), pp. 404–407.
-
K. Prachar (1957)
Primzahlverteilung.
Die Grundlehren der mathematischen Wissenschaften, Vol. 91, Springer-Verlag, Berlin-Göttingen-Heidelberg (German).
-
S. Pratt (2007)
Comoving coordinate system for relativistic hydrodynamics.
Phy. Rev. C 75, pp. (024907–1)–(024907–10).
-
T. Prellberg and A. L. Owczarek (1995)
Stacking models of vesicles and compact clusters.
J. Statist. Phys. 80 (3–4), pp. 755–779.
-
W. H. Press and S. A. Teukolsky (1990)
Elliptic integrals.
Computers in Physics 4 (1), pp. 92–96.
-
Prime Pages (website)
-
P. J. Prince (1975)
Algorithm 498: Airy functions using Chebyshev series approximations.
ACM Trans. Math. Software 1 (4), pp. 372–379.
-
M. H. Protter and C. B. Morrey (1991)
A First Course in Real Analysis.
2nd edition, Undergraduate Texts in Mathematics, Springer-Verlag, New York.
-
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev (1986a)
Integrals and Series: Elementary Functions, Vol. 1.
Gordon & Breach Science Publishers, New York.
-
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev (1986b)
Integrals and Series: Special Functions, Vol. 2.
Gordon & Breach Science Publishers, New York.
-
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev (1990)
Integrals and Series: More Special Functions, Vol. 3.
Gordon and Breach Science Publishers, New York.
-
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev (1992a)
Integrals and Series: Direct Laplace Transforms, Vol. 4.
Gordon and Breach Science Publishers, New York.
-
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev (1992b)
Integrals and Series: Inverse Laplace Transforms, Vol. 5.
Gordon and Breach Science Publishers, New York.
-
J. D. Pryce (1993)
Numerical Solution of Sturm-Liouville Problems.
Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York.
-
M. Puoskari (1988)
A method for computing Bessel function integrals.
J. Comput. Phys. 75 (2), pp. 334–344.