A Generalization of Class of Humbert - Hermite Polynomials

Authors

DOI:

https://doi.org/10.18311/jims/2022/25345

Keywords:

Hermite Polynomials, Humbert Polynomials, Gegenbauer Polynomials, Legendre Polynomials, Chebyshev Polynomials, Hypergeometric Function.

Abstract

A generalization of Humbert-Hermite polynomials is de?ned in this paper. Moreover, several generalizations of Hermite-Gegenbauer polynomials, Hermite-Legendre and Hermite-Chebyshev polynomials are established.

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References

E. T. Bell, Exponential polynomials, Ann. of Math., 35(1934), 258-277.

A. Chaturvedi, and Rai, P., Generalized Hermite-based Apostol-Bernoulli, Euler, Genocchi polynomials and their relations, Journal of Indian Mathematical Society, 87(1-2)(2020), 9-21.

J. Choi, Notes on formal manipulations ofdouble series, Commun. Korean Math. Soc., 18(4) (2003), 781-789.

Dattoli G., Germano B. and Ricci P. E., Hermite polynomials with more than two variables and associated bi-orthogonal functions, Integral Transforms and Special Functions, 20(1) (2009), 17-22.

G. Dattoli, S. Lorenzutta and C. Cesarano, Finite sums and generalized forms of Bernoulli polynomials, Rendiconti di Mathematica, 19(1999), 385–391.

G. B. Djordjevi´c, A generalization of Gegenbauer polynomial with two variables, Indian J. Pure Appl. Math., (To appear).

T. Kim, j. Choi, Y. H. Kim and C. S. Ryoo, On q-Bernstein and q-Hermite polynomials, Proc. Jangjeon Math. Soc., 14(A202) (2011), 215–221.

G. V. Milovanovi´c and G. B. Djordjevi´c, On some properties of Humberts polynomials-I, Fibonacci Quart., 25(1987), 356–360.

M. A. Pathan and M. A. Khan, On polynomials associated with Humberts polynomials, Publ. Inst. Math., (Beograd), 62(76) (1997), 53–62.

M. A. Pathan and N. U. Khan, A uni?ed presentation of a class of generalized Humbert Polynomials in two variables, ROMAI J., 11(2) (2015), 185–199.

M. A. Pathan and W. Khan, On a class of Humbert-Hermite polynomials, Novi Sad J. Math., 51(1) (2021), 1–11.

Y. Simsek and M. Acikgoz, A new generating function of (q?)Bernstein-type polynomials and their interpolation function, Abstract and Applied Analysis, 2010 (2010), Article ID 769095, 12 Pages.

Published

2022-08-23

How to Cite

Batra, S., & Rai, P. (2022). A Generalization of Class of Humbert - Hermite Polynomials. The Journal of the Indian Mathematical Society, 89(3-4), 227–236. https://doi.org/10.18311/jims/2022/25345