A General Inversion Pair and p-deformation of Askey Scheme

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Authors

  • Rajesh V. Savalia
     Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology, Changa-388 421, Dist: Anand ,IN
  • B. I. Dave
     Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390 002 ,IN

DOI:

https://doi.org/10.18311/jims/2019/22515

Keywords:

p-Gamma function, p-Pochhammer symbol, p-Deformed polynomials, Inverse series relation
05A19, 33C20, 33C45, 33C99

Abstract

The present work incorporates the general inverse series relations involving p-Pochhammer symbol and p-Gamma function. A general class of p-polynomials is introduced by means of this general inverse pair which is used to derive the generating function relations and summation formulas for certain p-polynomials belonging to this general class. This includes the p-deformation of Jacobi polynomials, the Brafman polynomials and Konhauser polynomials. Moreover, the orthogonal polynomials of Racah and those of Wilson are also provided p-deformation by means of the general inversion pair. The generating function relations and summation formulas for these polynomials are also derived. We then emphasize on the combinatorial identities and obtain their p-deformed versions.

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Published

2019-08-22

How to Cite

Savalia, R. V., & Dave, B. I. (2019). A General Inversion Pair and p-deformation of Askey Scheme. The Journal of the Indian Mathematical Society, 86(3-4), 296–314. https://doi.org/10.18311/jims/2019/22515

Issue

Volume 86, Issue 3-4, July-December 2019

Section

Articles

License

Copyright (c) 2019 Rajesh V. Savalia, B. I. Dave

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2018-10-16
Accepted 2019-03-20
Published 2019-08-22

 

References

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