We introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the ${}_6\f_5$ summation formula of F.~H.~Jackson and the $q$-Dixon sum. We also give $q$-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.

Keywords:

Basic hypergeometric series, balanced series, very well-poised series, integral representations, Al-Salam-Chihara polynomials. Basic hypergeometric series, balanced series, very well-poised series, integral representations, Al-Salam-Chihara polynomials.

MSC Classifications:

33D20, 33D60 show english descriptions unknown classification 33D20
Basic hypergeometric integrals and functions defined by them 33D20 - unknown classification 33D20
33D60 - Basic hypergeometric integrals and functions defined by them

top of page | contact us | social media | privacy | site map