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Finite bivariate biorthogonal $N$-Konhauser polynomials

Esra Güldoğan Lekesiz, Bayram Çekim, Mehmet Ali Özarslan

Abstract

A new set of finite 2D biorthogonal polynomials is defined using the finite orthogonal polynomials $N_{n}^{(p)}(w)$ and the Konhauser polynomials. We present a connection between this finite 2D biorthogonal set and the generalized Laguerre-Konhauser polynomials. Also, we obtain several applications of finite bivariate biorthogonal $N$-Konhauser polynomials.

Finite bivariate biorthogonal $N$-Konhauser polynomials

Abstract

A new set of finite 2D biorthogonal polynomials is defined using the finite orthogonal polynomials and the Konhauser polynomials. We present a connection between this finite 2D biorthogonal set and the generalized Laguerre-Konhauser polynomials. Also, we obtain several applications of finite bivariate biorthogonal -Konhauser polynomials.

Paper Structure

This paper contains 8 sections, 28 theorems, 139 equations.

Table of Contents

  1. Introduction
  2. The finite bivariate biorthogonal N - Konhauser polynomials
  3. Some properties for the fNKp
  4. Generating functions for the first set of fNKp
  5. Some recurrence relations and partial differential equations for the fNKp
  6. Operational and integral representations for the first set of fNKp
  7. Laplace transform and fractional calculus operators for the first set of fNKp
  8. A new class of finite 2D biorthogonal functions derived from fKNp

Key Result

Theorem 1

Assume that $\varpi(w)$ is a weight function over the interval $(d_{1},d_{2})$, and $u(w)$ and $g(w)$ are basic polynomials corresdponding to the polynomials $U_{s}(w)$ and $G_{n}(w)$, respectively. For $s,n\in\mathbb{N} _{0}$, so that and are provided Konhauser2.

Theorems & Definitions (38)

  • Theorem 1
  • Theorem 2
  • Definition 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8
  • Remark 9
  • Theorem 10
  • ...and 28 more