Buchholz polynomials: a family of polynomials relating solutions of confluent hypergeometric and Bessel equations

The expansion given by H. Buchholz, that allows one to express the regular confluent hypergeometric function M( a, b, z) as a series of modified Bessel functions with polynomial coefficients, is generalized to any solution of the confluent hypergeometric equation, by using a differential recurrence...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 1999-01, Vol.101 (1), p.237-241
Main Authors: Abad, Julio, Sesma, Javier
Format: Article
Language:English
Subjects:
Buchholz polynomials
Confluent hypergeometric function
Exact sciences and technology
Mathematical analysis
Mathematics
Modified Bessel function
Real functions
Sciences and techniques of general use
Special functions
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Description
Summary:The expansion given by H. Buchholz, that allows one to express the regular confluent hypergeometric function M( a, b, z) as a series of modified Bessel functions with polynomial coefficients, is generalized to any solution of the confluent hypergeometric equation, by using a differential recurrence obeyed by the Buchholz polynomials.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(99)00226-5