A cubic transformation formula for 2F1(1/3, 2/3; 1; z) and some arithmetic convolution formulae

被引：9

作者：

Williams, KS ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ctr Res Algebra & Number Theory, Ottawa, ON K1S 5B6, Canada

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2004年 / 137卷

关键词：

D O I：

10.1017/S0305004104007832

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A cubic transformation formula for the hypergeometric function F-2(1) (1/3, 2/3; 1; z) is proved. As an application of this formula a number of arithmetic convolution sums are evaluated. For example, Melfi's formula, [GRAPHICS] is proved without the use of modular forms.

引用

页码：519 / 539

页数：21

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