p-Deformation of a General Class of Polynomials and its Properties

Jump To References Section

Authors

  • Rajesh V. Savalia
     ,IN
  • B. I. Dave
     ,IN

DOI:

https://doi.org/10.18311/jims/2018/17945

Keywords:

General Class of p-deformed Polynomials, p-Deformed Inverse Series Relation, p-Deformed combinatorial identities

Abstract

The work incorporates the extension of the Srivastava-Pathan's generalized polynomial by means of p-generalized gamma function: Γ<sub>p</sub> and Pochhammer p-symbol (x)<sub>n,p</sub> due to Rafael Dıaz and Eddy Pariguan [Divulgaciones Mathematicas Vol.15, No. 2(2007), pp. 179-192]. We establish the inverse series relation of this extended polynomial with the aid of general inversion theorem. We also obtain the generating function relations and the differential equation. Certain p-deformed combinatorial identities are illustrated in the last section.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2018-01-04

How to Cite

Savalia, R. V., & Dave, B. I. (2018). p-Deformation of a General Class of Polynomials and its Properties. The Journal of the Indian Mathematical Society, 85(1-2), 226–240. https://doi.org/10.18311/jims/2018/17945

Issue

Volume 85, Issue 1-2, January-June 2018

Section

Articles

License

Copyright (c) 2018 Rajesh V. Savalia, B. I. Dave

Creative Commons License

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

Crossref
Scopus
Google Scholar
Europe PMC
Received 2017-09-07
Accepted 2023-01-30
Published 2018-01-04

 

References

Manisha Dalbhide. Generalization of certain ordinary and basic polynomials system and their properties, Ph. D. Thesis. The Maharaja Sayajirao University of Baroda, (2004), ISBN 978-1339-36594-7, ProQuestLLC, Ann Arbor, MI 48106, USA, 2015.

Rafael Diaz and Eddy Pariguan. Quantum symmetric functions, Communications in Algebra, 33(6) (2005), 1947-1978.

Rafael Diaz and Eddy Pariguan. On hypergeometric function and pochhammer k-symbol. Divulgaciones Mathematicas, 15(2) (2007), 179-192.

Rafael Diaz and Carolina Teruel. q,k-generalized gamma and beta function. Journal of Nonlinear Mathematical Physics, 12(1) (2005), 118-134.

D. Freed L. Jerey J. Morgan D. Morrison P. Deligne, P. Etingof and E. Witten. Quantum elds and strings:a course for mathematicians. American Mathematical Society, 1999.

E. D. Rainville. Special funtions, The Macmillan Company, New York, 1960.

John Riordan. Combinatorial Identities, John Willey and Sons. Inc., 1868.

H. M. Srivastava. The weyl fractional integral of a general class of polynomials. Boll. Un. Mat. Ital., 6(2B) (1983), 219-228.

H. M. Srivastava and H. L. Manocha. A treatise on generating function, Ellis horwood Limited, John Willey and Sons, 1984.