Numerical evaluation of the gauss hypergeometric function with the hypergeo package

R Journal

Volumn 7, Issue 2, 2015, Pages 81-88

  Hankin, Robin K S ^a  

^a AUCKLAND UNIVERSITY OF TECHNOLOGY   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84954155022     PISSN: None     EISSN: 20734859     Source Type: Journal    
DOI: 10.32614/rj-2015-022     Document Type: Article

References (22)

1. M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions. Dover, New York, 1965. [p81, 82, 84, 85, 86]
2. K. Alder, A. S. Bohr, T. Huus, B. Mottelson, and A. Winther. Study of nuclear structure by electromagnetic excitation with accelerated ions. Reviews of Modern Physics, 28:432, 1956. [p81]
3. W. Becken and P. Schmelcher. The analytic continuation of the Gaussian hypergeometric function 2F1 (a, b; c; z) for arbitrary parameters. Journal of Computational and Applied Mathematics, 126:449-478, 2000. [p86, 87]
4. D. S. Bove et al. appell: Compute Appell's F1 Hypergeometric Function, 2013. URL https://CRAN.R-project. org/package=appell. R package version 0.0-4. [p82]
5. W. Buhring. An analytic continuation of the hypergeometric series. SIAM Journal on Mathematical Analysis, 18(3):884-889, 1987. [p85, 87]
6. A. Cuyt et al. Handbook of Continued Fractions for Special Functions. Springer-Verlag, 2008. [p82]
7. A. I. Davydychev and M. Y. Kalmykov. Massive Feynman diagrams and inverse binomial sums. Nuclear Physics B, 699:3-64, 2004. [p81]
8. Á. de la Cruz-Dombriz and A. Dobado. f (r) gravity without a cosmological constant. Physical Review D, 74(8-15), Oct. 2006. [p81]
9. R. C. Forrey. Computing the hypergeometric function. Journal of Computational Physics, 137:79-100, 1997. [p82, 85, 87]
10. M. Galassi et al. GNU Scientific Library, 2013. URL http://www.gnu.org/software/gsl/. Reference Manual edition 1.16. [p82]
11. R. K. S. Hankin. Introducing elliptic, an R package for elliptic and modular functions. Journal of Statistical Software, 15, Feb. 2006a. [p86]
12. R. K. S. Hankin. Special functions in R: Introducing the gsl package. R News, 6, Oct. 2006b. [p82]
13. F. Johansson et al. mpmath: A Python Library for Arbitrary-Precision Floating-Point Arithmetic (Version 0.18), Oct. 2013. http://code.google.com/p/mpmath/. [p85]
14. Maxima. Maxima, a Computer Algebra System. Version 5.34.1. http://maxima.sourceforge.net/, 2014. URL http://maxima.sourceforge.net/. [p82]
15. N. Michel and M. V. Stoitsov. Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions. Computer Physics Communictions, 178:535-551, 2008. URL http://arxiv.org/abs/0708.0116v1. [p81, 82, 87]
16. M. Petkovšek, H. S.Wilf, and D. Zeilberger. A = B. A. K. Peters, Ltd., 1997. [p81]
17. W. H. Press, S. A. Teukolsky,W. T. Vetterling, and B. P. Flannery. Numerical recipes in C: The art of scientific computing, 1992. [p85]
18. J. B. Seaborn. Hypergeometric Functions and Their Applications. Springer-Verlag, 1991. [p81]
19. K. Soetaert, T. Petzoldt, and R. W. Setzer. Solving differential equations in R: Package desolve. Journal of Statistical Software, 33(9):1-25, 2010. URL http://www.jstatsoft.org/v33/i09. [p84]
20. W. Stein et al. Sage Mathematics Software (Version 5.8). The Sage Development Team, 2015. URL http://www.sagemath.org. [p82]
21. B. Thaller. Visualization of complex functions. The Mathematica Journal, 7(2):163-180, 1998. [p86]
22. S. Wolfram. The hypergeometric function, 2014. File Hypergeometric2F1.pdf, downloaded from http:/functions.wolfram.com/HypergeometricFunctions/. [p85]