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Rodrigues Formulas and Generating Functions

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Hypergeometric Summation

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Abstract

In this chapter we use the algorithms of the preceding chapter to obtain holonomic equations for function families given by Rodrigues type formulas and generating functions.

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Notes

  1. 1.

    Their corrected formula \({\fancyscript{D}}_q^n f(x)=\frac{(-1)^n\,q^{-{\big (\begin{array}{c}{n}\\ {2}\\ \end{array}\big )}}}{(1-q)^n\,x^n}\sum \limits _{r=0}^n(-1)^r \left[ \begin{array}{c}\!\!n\!\!\\ \!\!r\!\!\end{array}\right] _{q}\,q^{{\big (\begin{array}{c}{r}\\ {2}\\ \end{array}\big )}}\,f(q^{n-r}\,x)\) follows from (13.10) by changing the order of summation \(r=n-k\).

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Authors and Affiliations

  1. Fachbereich 10 Mathematik und Naturwissenschaften, Universität Kassel, Heinrich-Plett-Str. 40, 34132, Kassel, Germany

    Wolfram Koepf

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  1. Wolfram Koepf
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Koepf, W. (2014). Rodrigues Formulas and Generating Functions. In: Hypergeometric Summation. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-6464-7_13

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