Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Hans Weber
Open Mathematics, Tome 5 (2007), p. 415-427 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:269025 
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Hans Weber. Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula. Open Mathematics, Tome 5 (2007) pp. 415-427. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0004-6/

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