The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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


Affiliations
1 Charotar University of Science and Technology, Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, India
2 The Maharaja Sayajirao University of Baroda, Department of Mathematics, Vadodara, India
     

   Subscribe/Renew Journal


The work incorporates the extension of the Srivastava-Pathan’s generalized polynomial by means of p-generalized gamma function: Γp and Pochhammer p-symbol (x)n,p 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.

Keywords

General Class of p-Deformed Polynomials, p-Deformed Inverse Series Relation, p-Deformed Combinatorial Identities.
Subscription Login to verify subscription
User
Notifications
Font Size


  • 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.


Abstract Views: 309

PDF Views: 0




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

Abstract Views: 309  |  PDF Views: 0

Authors

Rajesh V. Savalia
Charotar University of Science and Technology, Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, India
B. I. Dave
The Maharaja Sayajirao University of Baroda, Department of Mathematics, Vadodara, India

Abstract


The work incorporates the extension of the Srivastava-Pathan’s generalized polynomial by means of p-generalized gamma function: Γp and Pochhammer p-symbol (x)n,p 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.

Keywords


General Class of p-Deformed Polynomials, p-Deformed Inverse Series Relation, p-Deformed Combinatorial Identities.

References