Abstract
In the present work, a pair of general inverse matrix series relations is established, and thereby a general class of matrix polynomials is introduced. This class generalizes the extended Jacobi polynomials and their particular cases such as the polynomials of Brafman, Jacobi, Chebyshev, and Legendre. It is further shown that this pair also gives rise to the matrix forms of the Wilson polynomials and the Racah polynomials. For these polynomials, the generating matrix function relations as well as the matrix summation formulas are deduced from their respective inverse pairs. Certain inverse pairs belonging to the Gould classes and the Legendre-Chebyshev classes due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968] are also extended to matrix forms.
( Communicated by Marek Balcerzak )
Acknowledgement
The authors are indebted to the referee for the valuable suggestions and indicating the corrections for the improvement of the manuscript.
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Articles in the same Issue
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
- The symmetric 4-Player gambler’s problem with unequal initial stakes
- Enveloping action: Convergence spaces