2019
DOI: 10.3390/sym11020151
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Two Variables Shivley’s Matrix Polynomials

Abstract: The principal object of this paper is to introduce two variable Shivley's matrix polynomials and derive their special properties. Generating matrix functions, matrix recurrence relations, summation formula and operational representations for these polynomials are deduced. Finally, Some special cases and consequences of our main results are also considered.

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Cited by 12 publications
(6 citation statements)
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“…Definition 3 (see [20,23]). Let A and B be positive stable matrices in C r×r ; then, the Jacobi matrix polynomial (JMP)…”
Section: Definitionmentioning
confidence: 99%
“…Definition 3 (see [20,23]). Let A and B be positive stable matrices in C r×r ; then, the Jacobi matrix polynomial (JMP)…”
Section: Definitionmentioning
confidence: 99%
“…Recently, considerable attention has been paid to fractional integrals associated with special matrix functions and orthogonal matrix polynomials, due mainly to their usefulness and applications in various research subjects (see, e.g., [8,14,18,19,[36][37][38][39][40][41][42][43][44][45] and the references cited therein). [46] investigated the revival of the Bessel polynomials and the generalized Bessel polynomials (GBPs) whose explicit forms are given, respectively, by…”
Section: Introductionmentioning
confidence: 99%
“…Recently, many works on the Bessel function theory have been achieved, for example, by Agarwal et al, 20 Cortés et al, 21 Mondal and Akel, 22 Albayrak et al, 23 and Mubeen et al 24 Nowadays, special matrix functions have variety of uses in the field of probability theory, fractional operators, modeling of groundwater pumping, quantum algebraic techniques, and engineering sciences. Very recently, many authors work on these functions (for details, see the works of Abdalla, [25][26][27] Bakhet et al, 28 Dwivedi and Sahai, 29,30 Ismail et al, 31 He et al, 32,33 Khammash et al, 34 Srivastava et al, 35 and Zayed et al 36,37 ). One particular special matrix function that frequently appears in the recent studies and applications is the Bessel matrix function, which has been introduced and discussed in previous studies.…”
Section: Introductionmentioning
confidence: 99%