Finite Bivariate Biorthogonal M-Konhauser Polynomials (2409.03355v3)

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.