The Journal of the Indian Mathematical Society

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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
     

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

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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