Mathematics > Combinatorics
[Submitted on 17 May 2018]
Title:Extensions of Ramanujan's reciprocity theorem and the Andrews--Askey integral
View PDFAbstract:Ramanujan's reciprocity theorem may be considered as a three-variable extension of Jacobi's triple product identity. Using the method of $q$-partial differential equations, we extend Ramanujan's reciprocity theorem to a seven-variable reciprocity formula. The Andrews--Askey integral is a $q$-integral having four parameters with base $q$. Using the same method we extend the Andrews--Askey integral formula to a $q$-integral formula which has seven parameters with base $q$.
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