A note on q-difference equations for Ramanujan's integrals

作者：Cao, Jian^*

来源：Ramanujan Journal, 2019, 48(1): 63-73.

DOI：10.1007/s11139-017-9987-1

• Solutions of q-difference equation
• Generating function
• Al-Salam-Carlitz polynomial
• Ramanujan's integral

This short paper derives the relationship between solutions of q-difference equations and generating functions for q-orthogonal polynomials. The key of the method is to obtain the expression of certain q-orthogonal polynomials as solutions of q-difference equations. In addition, we show how to generalize Ramanujan's integrals by the technique of q-difference equation. More over, we find two generalized q-Chu-Vandermonde formulas from the perspective of the method of q-difference equations.

• 出版日期2019-1
• 单位杭州师范大学