An extension of the non-terminating ₆φ₅ summation and the Askey–Wilson polynomials

Abstract

In this paper, we give an extension of the non-terminating summation using the method of q-exponential operator and difference equation. This extended formula allows us to give a new generating function of the Askey–Wilson polynomials.

Keywords:

• q-series
• ₆φ₅ summation
• q-derivative
• q-difference equation
• q-exponential operator
• Askey–Wilson's polynomials

2000 Mathematics Subject Classification::

• 05A30
• 33D15
• 33D45
• 11E25

Acknowledgement

This work was supported by the National Science Foundation of China, PCSIRT, Innovation Program of Shanghai Municipal Education Commission and Shanghai Leading Academic Discipline Project, Project No. B407.