Classification of hypergeometric identities for pi and other logarithms of algebraic numbers.

Abstract:

:This paper provides transcendental and algebraic framework for the classification of identities expressing pi and other logarithms of algebraic numbers as rapidly convergent generalized hypergeometric series in rational parameters. Algebraic and arithmetic relations between values of p+1Fp hypergeometric functions and their values are analyzed. The existing identities are explained, and new exhaustive classes of new ones are presented.

authors

Chudnovsky DV,Chudnovsky GV

doi

10.1073/pnas.95.6.2744

subject

Has Abstract

pub_date

1998-03-17 00:00:00

pages

2744-9

issue

6

eissn

0027-8424

issn

1091-6490

journal_volume

95

pub_type

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