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/