References

The following is a non-comprehensive list of works used in the development of mpmath or cited for examples or mathematical definitions used in this documentation. References not listed here can be found in the source code.

[AbramowitzStegun]

M Abramowitz & I Stegun. Handbook of Mathematical Functions, 9th Ed., Tenth Printing, December 1972, with corrections (electronic copy: http://people.math.sfu.ca/~cbm/aands/)

[Bailey]

D H Bailey. “Tanh-Sinh High-Precision Quadrature”, http://crd.lbl.gov/~dhbailey/dhbpapers/dhb-tanh-sinh.pdf

[BenderOrszag]

C M Bender & S A Orszag. Advanced Mathematical Methods for Scientists and Engineers, Springer 1999

[BorweinBailey]

J Borwein, D H Bailey & R Girgensohn. Experimentation in Mathematics - Computational Paths to Discovery, A K Peters, 2003

[BorweinBorwein]

J Borwein & P B Borwein. Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, Wiley 1987

[BorweinZeta]

P Borwein. “An Efficient Algorithm for the Riemann Zeta Function”, http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf

[CabralRosetti]

L G Cabral-Rosetti & M A Sanchis-Lozano. “Appell Functions and the Scalar One-Loop Three-point Integrals in Feynman Diagrams”. http://arxiv.org/abs/hep-ph/0206081

[Carlson]

B C Carlson. “Numerical computation of real or complex elliptic integrals”. http://arxiv.org/abs/math/9409227v1

[Corless]

R M Corless et al. “On the Lambert W function”, Adv. Comp. Math. 5 (1996) 329-359. http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf

[DLMF]

NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/

[GradshteynRyzhik]

I S Gradshteyn & I M Ryzhik, A Jeffrey & D Zwillinger (eds.), Table of Integrals, Series and Products, Seventh edition (2007), Elsevier

[GravesMorris]

P R Graves-Morris, D E Roberts & A Salam. “The epsilon algorithm and related topics”, Journal of Computational and Applied Mathematics, Volume 122, Issue 1-2 (October 2000)

[MPFR]

The MPFR team. “The MPFR Library: Algorithms and Proofs”, http://www.mpfr.org/algorithms.pdf

[Slater]

L J Slater. Generalized Hypergeometric Functions. Cambridge University Press, 1966

[Spouge]

J L Spouge. “Computation of the gamma, digamma, and trigamma functions”, SIAM J. Numer. Anal. Vol. 31, No. 3, pp. 931-944, June 1994.

[SrivastavaKarlsson]

H M Srivastava & P W Karlsson. Multiple Gaussian Hypergeometric Series. Ellis Horwood, 1985.

[Vidunas]

R Vidunas. “Identities between Appell’s and hypergeometric functions”. http://arxiv.org/abs/0804.0655

[Weisstein]

E W Weisstein. MathWorld. http://mathworld.wolfram.com/

[WhittakerWatson]

E T Whittaker & G N Watson. A Course of Modern Analysis. 4th Ed. 1946 Cambridge University Press

[Wikipedia]

Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Main_Page

[WolframFunctions]

Wolfram Research, Inc. The Wolfram Functions Site. http://functions.wolfram.com/