Abstract

A special singular limit \(\omega_1/\omega_2 \to 1\) is considered for the Faddeev modular quantum dilogarithm (hyperbolic gamma function) and the corresponding hyperbolic integrals. It brings a new class of hypergeometric identities associated with bilateral sums of Mellin–Barnes type integrals of particular Pochhammer symbol products.

中文翻译：

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有理超几何恒等式

摘要

对于 Faddeev 模量子对数（双曲伽马函数）和相应的双曲积分，考虑了一个特殊的奇异极限\(\omega_1/\omega_2 \to 1\) 。它带来了一类新的超几何恒等式，与特定 Pochhammer 符号产品的 Mellin-Barnes 类型积分的双边和相关。