Numerical methods for the computation of the confluent and Gauss hypergeometric functions
Tóm tắt
Tài liệu tham khảo
Abad, J., Sesma, J.: Computation of the regular confluent hypergeometric function. The Mathematica Journal 5, 74–76 (1995)
Abramowitz, M., Stegun, I. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards (1970)
Andrews, G.E., Askey, R., Roy, R.: Special Functions, vol. 71 of Mathematics and its Applications. Cambridge University Press (1999)
Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi , F.G.: Higher Transcendental Functions, vol. I. McGraw–Hill (1953)
Ferreira, C., López, J. L., Sinusía, E. P.: The Gauss hypergeometric function F(a,b;c;z) for large c. J. Comput. Appl. Math. 197, 568–577 (2006)
Gil, A., Segura, J.: Algorithm 819: AIZ, BIZ: Two Fortran 77 routines for the computation of complex Airy functions. Trans. Math. Softw. 28, 325–336 (2002)
Gil, A., Segura, J., Temme, N.M.: Numerical Methods for Special Functions. Society for Industrial and Applied Mathematics (2007)
Gil, A., Segura, J., Temme, N.M.: Parabolic cylinder function W(a,x) and its derivative. ACM Trans. Math. Softw. 38 (2011). Article 6
Godfrey, P.: A note on the computation of the convergent Lanczos complex gamma approximation (2001), available at http://www.numericana.com/answer/info/godfrey.htm
Hochstadt, H.: The Functions of Mathematical Physics. Wiley (1971)
Hsu , Y. P.: Development of a Gaussian hypergeometric function code in complex domains. Int. J. Modern Phys. C 4, 805–840 (1993)
Ibrahim, A.K., Rakha, M.A.: Contiguous relations and their computations for 2 F 1 hypergeometric series. Comput. Math. Appl. 56, 1918–1926 (2008)
Kalla, S.L.: On the evaluation of the Gauss hypergeometric function. Compt. Rendus l’Acad. Bulgare Sci. 45, 35–36 (1992)
López, J. L., Pagola, P.J: The confluent hypergeometric functions M(a,b;z) and U(a,b;z) for large b and z. J. Comput. Appl. Math. 233, 1570–1576 (2010)
Luke, Y.L.: The Special Functions and their Approximations, vol. I. Academic Press (1969)
Luke , Y.L.: The Special Functions and their Approximations, vol. II. Academic Press (1969)
Pearson, J.: Computation of Hypergeometric Functions, Dissertation, MSc in Mathematical Modelling and Scientific Computing, University of Oxford (2009), available at https://sites.google.com/site/johnpearsonmaths/research
Potts, P.J.: Computable real arithmetic using linear fractional transformations. Report, Department of Computing, Imperial College of Science, Technology and Medicine, London (1996), available at http://citeseer.ist.psu.edu/potts96computable.html
Press, W.A., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing. 3rd edn. Cambridge University Press (2007)
Seaborn, J.B.: Hypergeometric Functions and their Applications. Springer-Verlag (1991)
Slater, L.J.: Confluent Hypergeometric Functions. Cambridge University Press (1960)
Slater, L.J.: Generalized Hypergeometric Functions. Cambridge University Press (1966)
Temme, N.M.: Special Functions: An Introduction to the Classical Functions of Mathematical Physics. Wiley (1996)
Digital Library of Mathematical Functions, National Institute of Standards and Technology, available at http://dlmf.nist.gov/
Matlab, The Mathworks Inc., Version R2015a (2015)
Mathematica, Wolfram Research, Inc., Mathematica, Version 8.0 (2010)
The NAG Toolbox for Matlab, The Numerical Algorithms Group (2013)