# Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

Open Mathematics (2007)

- Volume: 5, Issue: 2, page 415-427
- ISSN: 2391-5455

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topHans Weber. "Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula." Open Mathematics 5.2 (2007): 415-427. <http://eudml.org/doc/269025>.

@article{HansWeber2007,

abstract = {Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.},

author = {Hans Weber},

journal = {Open Mathematics},

keywords = {Polynomials with Rodrigues formula; solutions of hypergeometric-type differential equation; generating function in closed form; recursion relations; addition theorem; polynomials with Rodrigues formula},

language = {eng},

number = {2},

pages = {415-427},

title = {Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula},

url = {http://eudml.org/doc/269025},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Hans Weber

TI - Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

JO - Open Mathematics

PY - 2007

VL - 5

IS - 2

SP - 415

EP - 427

AB - Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.

LA - eng

KW - Polynomials with Rodrigues formula; solutions of hypergeometric-type differential equation; generating function in closed form; recursion relations; addition theorem; polynomials with Rodrigues formula

UR - http://eudml.org/doc/269025

ER -

## References

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- [7] M. Abramowitz and I.A. Stegun: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, 2nd edition, New York, 1972.
- [8] I.S. Gradshteyn and I.M. Ryzhik: Table of Integrals, Series and Products, ed. A. Jeffrey, Acad. Press, San Diego, 2000. Zbl0981.65001

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