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arXiv · 2409.03355

Finite Bivariate Biorthogonal M-Konhauser Polynomials

Esra Güldoğan Lekesiz·Bayram Çekim·Mehmet Ali Özarslan
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Abstract

In this paper, we construct the pair of finite bivariate biorthogonal M-Konhauser polynomials, reduced to the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$, by choosing appropriate parameters in order to obtain a relation between the Jacobi Konhauser polynomials and this new finite bivariate biorthogonal polynomials $_{K}M_{n;\upsilon}^{(p,q)}(z,t)$ similar to the relation between the classical Jacobi polynomials $P_{n}^{(p,q)}(t)$ and the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$. Several properties like generating function, operational/integral representation are derived and some applications like fractional calculus, Fourier transform and Laplace transform are studied thanks to that new transition relation and the definition of finite bivariate M-Konhauser polynomials.

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Esra Güldoğan Lekesiz, Bayram Çekim, Mehmet Ali Özarslan. 2024-09-05. Finite Bivariate Biorthogonal M-Konhauser Polynomials. https://arxiv.org/abs/2409.03355

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