Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 875-893.

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

Jinfa Cheng*(),Lukun Jia   

  1. School of Mathematical Science, Xiamen University, Fujian Xiamen 361005
  • Received:2017-03-14 Online:2019-08-26 Published:2019-09-11
  • Contact: Jinfa Cheng
  • Supported by:
    福建省自然科学基金(2016J01032);the Natural Science Foundation of Fujian Province(2016J01032)


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

CLC Number: 

  • O174.6