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A General Inversion Pair and ρ-deformation of Askey Scheme


Affiliations
1 Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa-388 421, Dist: Anand, India
2 Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara-390 002, India
     

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The present work incorporates the general inverse series relations involving p-Pochhammer symbol and p-Gamma function. A general class of ρ-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 ρ-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 ρ-deformed versions.

Keywords

ρ-Gamma Function, ρ-Pochhammer Symbol, ρ-Deformed Polynomials, Inverse Series Relation.
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  • A General Inversion Pair and ρ-deformation of Askey Scheme

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Authors

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

Abstract


The present work incorporates the general inverse series relations involving p-Pochhammer symbol and p-Gamma function. A general class of ρ-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 ρ-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 ρ-deformed versions.

Keywords


ρ-Gamma Function, ρ-Pochhammer Symbol, ρ-Deformed Polynomials, Inverse Series Relation.

References





DOI: https://doi.org/10.18311/jims%2F2019%2F22515