Bilateral generating functions for the Chan–Chyan–Srivastava polynomials and the generalized Lauricella functions

Abstract

In some recent investigations involving differential operators for generalized Lagrange polynomials, Chan et al. [The Lagrange polynomials in several variables, Integral Transforms Spec. Funct. 12 (2001), pp. 139–148] encountered and proved a certain summation identity for the Lagrange polynomials in several variables, which are popularly known as the Chan–Chyan–Srivastava polynomials. In the present paper, we investigate several families of bilateral generating functions for the Chan–Chyan–Srivastava polynomials and the (Srivastava–Daoust) generalized Lauricella functions.

Keywords:

• Lagrange polynomials
• Chan–Chyan–Srivastava polynomials
• Lauricella functions
• (Srivastava–Daoust) generalized Lauricella functions
• Kampé de Fériet function
• Appell’s functions
• Erkuş–Srivastava polynomials
• Srivastava’s theorem
• Riemann–Liouville fractional derivative
• Bilinear, bilateral and mixed multilateral generating functions

2010 Mathematics Subject Classification :

• Primary: 33C45
• 33C65
• Secondary: 26A33
• 33C05

Acknowledgement

The present investigation was supported, in part, by the National Science Council of the Republic of China under Grant NSC 99-2811-M-033-014.