Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral

2013/05/14 by Wei, Chuanan, Wang, Xiaoxia, Yan, Qinglun
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.2596

Abstract

By using two known transformation formulas for basic hypergeometric series, we establish a direct extension of Bailey's ₆ψ₆-series identity. Subsequently, it and Milne's identity are employed to drive multi-variable generalizations of Ramanujan's reciprocity formula. Then we utilize also Milne's identity to deduce a multi-variable generalization of the Askey-Wilson integral.

Related

• Several transformation formulas for basic hypergeometric series
• A Five-variable generalization of Ramanujan's reciprocity theorem
• Expansion Formulas of Basic Hypergeometric Series via the (1-xy,y-x)--Inversion and Its Applications
• Bailey Type Transforms and Applications
• Contiguous relations, continued fractions and orthogonality