Tbilisi Mathematical Journal

Finding hybrid families of special matrix polynomials associated with Sheffer sequences

Ghazala Yasmin, Shahid Ahmad Wani, and Hibah Islahi

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In this paper, three index three variable Hermite matrix based Sheffer polynomials (3I3VHMSP) are introduced by algebraic decomposition of exponential operators. The operational methods combined with the monomiality principle can be used to introduce 3I3VHMSP and also to establish rules of operational nature, framing the special polynomials within the context of particular solutions of generalized forms of partial differential equations of evolution type. The Appell and Sheffer sequences along with the operational formalism offer a powerful tool for investigation of the properties of a wide class of polynomials. Further, operational representation providing connections between 3I3VHMSP families and the known special polynomials are established, which are used to derive new identities and the results for the members of these new families. The approach presented is general.

Article information

Tbilisi Math. J., Volume 12, Issue 4 (2019), 43-59.

Received: 15 April 2019
Accepted: 23 September 2019
First available in Project Euclid: 3 January 2020

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Mathematical Reviews number (MathSciNet)

Primary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]
Secondary: 33C99: None of the above, but in this section 33E20: Other functions defined by series and integrals

3 index 3 varible Hermite matrix based Sheffer polynomials monomiality principle operational techniques


Yasmin, Ghazala; Ahmad Wani, Shahid; Islahi, Hibah. Finding hybrid families of special matrix polynomials associated with Sheffer sequences. Tbilisi Math. J. 12 (2019), no. 4, 43--59. doi:10.32513/tbilisi/1578020566. https://projecteuclid.org/euclid.tbilisi/1578020566

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