非一致格子上的超几何型差分方程:第二类解的Rodrigues型表示公式

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 875-893.

非一致格子上的超几何型差分方程:第二类解的Rodrigues型表示公式

程金发*(),贾鲁昆

厦门大学数学科学学院福建厦门 361005

收稿日期:2017-03-14 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 程金发 E-mail:jfcehng@xmu.edu.cn
基金资助:
福建省自然科学基金(2016J01032);the Natural Science Foundation of Fujian Province(2016J01032)

Hypergeometric Type Difference Equations on Nonuniform Lattices: Rodrigues Type Representation for the Second Kind Solution

Jinfa Cheng*(),Lukun Jia

School of Mathematical Science, Xiamen University, Fujian Xiamen 361005

Received:2017-03-14 Online:2019-08-26 Published:2019-09-11
Contact: Jinfa Cheng E-mail:jfcehng@xmu.edu.cn
Supported by:
福建省自然科学基金(2016J01032);the Natural Science Foundation of Fujian Province(2016J01032)

摘要/Abstract

摘要：

通过建立非一致格子上的二阶伴随方程，得到了非一致格子上超几何型差分方程第二类解的Rodrigues型表示公式，它们推广了经典Rodrigues公式.由此得到由经典Rodrigues公式和广义罗德里格斯公式线性组合而成的通解.

关键词: 特殊函数, 正交多项式, 伴随差分方程, 超几何型差分方程, 非一致格子

Abstract:

By building a second order adjoint equation, the Rodrigues type representation for the second kind solution of a second order difference equation of hypergeometric type on nonuniform lattices is given. The general solution of the equation in the form of a combination of a standard Rodrigues formula and a "generalized" Rodrigues formula is also established.

Key words: Special function, Orthogonal polynomial, Adjoint difference equation, Hypergeometric difference equations, Nonuniform lattice

中图分类号:

O174.6

程金发,贾鲁昆. 非一致格子上的超几何型差分方程:第二类解的Rodrigues型表示公式[J]. 数学物理学报, 2019, 39(4): 875-893.

Jinfa Cheng,Lukun Jia. Hypergeometric Type Difference Equations on Nonuniform Lattices: Rodrigues Type Representation for the Second Kind Solution[J]. Acta mathematica scientia,Series A, 2019, 39(4): 875-893.

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