On generating functions of modified Jacobi polynomials

Authors

  • Amartya Chongdar Bangabasi College.

DOI:

https://doi.org/10.22199/issn.0717-6279-5267

Keywords:

partial quasi-bilateral (or partial quasi-bilinear) generating relation, partial quasi-bilateral (or partial quasi-bilinear) generating function, modified Jacobi polynomial

Abstract

In this paper, the present author has made an attempt to present a generalization of the result on bilateral generating functions involving modified Jacobi polynomials, found derived in [1, 2], by means of the theory of one parameter group of continuous transformations and using the notion of partial quasi bilateral generating function [3] involving some special functions.

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Author Biography

  • Amartya Chongdar, Bangabasi College.

    Department of Mathematics.

References

A. K. Chongdar, “On a class of bilateral generating functions for certain special functions”, Proceedings of the Indian Academy of Sciences - Section A, vol. 95, no. 2, pp. 133–140, 1986. https://doi.org/10.1007/bf02881077

A. K. Chongdar and M. C. Mukkherjee, “On a class of bilateral generating functions of certain special functions”, Bulletin of the Institute of Mathematics, Academia Sinica, vol. 17, no. 1, pp. 67-73, 1989.

A. K. Mondal, “A unified group theoretic method of obtaining a more general class of generating relations from a given class of partial quasi-bilateral (or partial quasi-bilinear) generating relations involving some special functions”, Pure Mathematics Manuscript, vol. 10, pp. 121-132,1993.

A. K. Mondal, “Partial quasi bilateral generating function involving Laguerre and Gegenbauer polynomials (I)”, Pure Mathematics Manuscript, vol. 10, pp. 97-103,1993.

A. K. Mondal, “Partial quasi bilinear generating function involving Laguerre polynomials”, Pure Mathematics Manuscript, vol. 10, pp. 89-95, 1993.

L. Weisner, “Group-theoretic origin of certain generating function”, Pacific Journal of Mathematics, vol. 5, no. 6, pp. 1033–1039, 1955. https://doi.org/10.2140/pjm.1955.5.1033.

L. Weisner, “Generating functions for hermite functions”, Canadian Journal of Mathematics, vol. 11, pp. 141–147, 1959. https://doi.org/10.4153/cjm-1959-018-4

L. Weisner, “Generating functions for Bessel functions,” Canadian Journal of Mathematics, vol. 11, pp. 148–155, 1959. https://doi.org/10.4153/cjm-1959-019-1

S. Das, “On partial differential operators for Jacobi polynomials”, Pure Mathematics Manuscript, vol. 3, pp. 95-104, 1984.

S. K. Chatterjea and S. P. Chakrabarty, “A unified group-theoretic method of obtaining a more general class of generating relations from a given class of quasi-bilateral (or quasi-bilinear) generating relations involving special functions”, Pure Mathematics Manuscript, vol. 8, pp. 153-162, 1989.

E. D. Rainville, Special functions. New York: Chelsea publishing Co., 1960.

A. K, Chongdar and S. K. Chatterjea, “On a class of trilateral generating relations with Tchebycheff polynomials from the view point of one parameter group of continuous transformations”, Bulletin of the Calcutta Mathematical Society, vol. 73, pp. 127-140,1981.

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Published

2022-07-28

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Section

Artículos

How to Cite

[1]
“On generating functions of modified Jacobi polynomials”, Proyecciones (Antofagasta, On line), vol. 41, no. 4, pp. 923–932, Jul. 2022, doi: 10.22199/issn.0717-6279-5267.