有限双变量双正交 M-Konhauser 多项式
Finite Bivariate Biorthogonal M-Konhauser Polynomials
AI总结：
本文构造有限双变量双正交 M-Konhauser 多项式，建立其与 Jacobi Konhauser 多项式的转换关系，并推导生成函数、积分表示及分数阶微积分等应用。
摘要：
本文通过选取适当参数，构造了有限双变量双正交 M-Konhauser 多项式对，并将其约化为有限正交多项式 $M_{n}^{(p,q)}(t)$，以获得 Jacobi Konhauser 多项式与该新有限双变量双正交多项式 $_{K}M_{n;\upsilon}^{(p,q)}(z,t)$ 之间的关系，类似于经典 Jacobi 多项式 $P_{n}^{(p,q)}(t)$ 与有限正交多项式 $M_{n}^{(p,q)}(t)$ 之间的关系。借助该新的转换关系及有限双变量 M-Konhauser 多项式的定义，推导了生成函数、算子/积分表示等若干性质，并研究了分数阶微积分、傅里叶变换和拉普拉斯变换等应用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
