On a Transformation of Triple q-Series and Rogers-Hecke Type Series
Abstract
Using the method of the q-exponential differential operator, we give an extension of the Sears 4φ3 transformation formula. Based on this extended formula and a q-series expansion formula for an analytic function around the origin, we present a transformation formula for triple q-series, which includes several interesting special cases, especially a double q-series summation formula. Some applications of this transformation formula to Rogers-Hecke type series are discussed. More than 100 Rogers-Hecke type identities including Andrews' identities for the sums of three squares and the sums of three triangular numbers are obtained.
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