On a multivariable extension of the Humbert polynomials

AbstractIn this paper, we present some miscellaneous properties of the multivariable Humbert polynomials whose special cases include some well-known multivariable polynomials such as Chan-Chyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We give recurrence relations, addition formula and integral representation for them. Then, we obtain some partial differential equations for the products of the multivariable Humbert polynomials and some other multivariable polynomials. Furthermore, some special cases of the results presented in this study are also indicated.

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A Class of Laguerre-Based Generalized Humbert Polynomials

International Journal of Differential Equations ◽

10.1155/2021/4324466 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Saniya Batra ◽

Prakriti Rai

Keyword(s):

Additional Symmetry ◽

Research Areas ◽

Summation Formulas ◽

Differential Relations ◽

Humbert Polynomials

Several mathematicians have extensively investigated polynomials, their extensions, and their applications in various other research areas for a decade. Our paper aims to introduce another such polynomial, namely, Laguerre-based generalized Humbert polynomial, and investigate its properties. In particular, it derives elementary identities, recursive differential relations, additional symmetry identities, and implicit summation formulas.

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ON MATRIX POLYNOMIALS ASSOCIATED WITH HUMBERT POLYNOMIALS

The Pure and Applied Mathematics ◽

10.7468/jksmeb.2014.21.3.207 ◽

2014 ◽

Vol 21 (3) ◽

pp. 207-218

Author(s):

M.A. Pathan ◽

Maged G. Bin-Saad ◽

Fadhl Al-Sarahi

Keyword(s):

Matrix Polynomials ◽

Humbert Polynomials

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Generalized Humbert polynomials and second-order partial differential operators

Bulletin des Sciences Mathématiques ◽

10.1016/j.bulsci.2009.03.002 ◽

2009 ◽

Vol 133 (7) ◽

pp. 733-755

Author(s):

Abdlilah Bouali

Keyword(s):

Differential Operators ◽

Second Order ◽

Partial Differential ◽

Partial Differential Operators ◽

Humbert Polynomials

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On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2009/709386 ◽

2009 ◽

Vol 2009 ◽

pp. 1-21 ◽

Cited By ~ 5

Author(s):

Tian-Xiao He ◽

Peter J.-S. Shiue

Keyword(s):

Recurrence Relation ◽

Chebyshev Polynomials ◽

Recurrence Relations ◽

Linear Recurrence ◽

Lucas Numbers ◽

Polynomial Sequences ◽

Fibonacci And Lucas Numbers ◽

Linear Recurrence Relation ◽

Humbert Polynomials ◽

General Method

Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.

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On a Family of Multivariate Modified Humbert Polynomials

The Scientific World JOURNAL ◽

10.1155/2013/187452 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12

Author(s):

Rabia Aktaş ◽

Esra Erkuş-Duman

Keyword(s):

Generating Functions ◽

Special Cases ◽

Humbert Polynomials

This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials.

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