Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions

Expansions in terms of Bessel functions are considered of the Kummer function 1 F 1 ( a ; c , z ) (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic behavior of thes...

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Vydáno v:	Numerische Mathematik Ročník 116; číslo 2; s. 269 - 289
Hlavní autoři:	López, José Luis, Temme, Nico M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer-Verlag 01.08.2010 Springer
Témata:	Difference and functional equations, recurrence relations Exact sciences and technology Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical Analysis Numerical analysis. Scientific computation Numerical and Computational Physics Sciences and techniques of general use Simulation Special functions Theoretical Asymptotic expansions 33C15 65D20 33C10 Kummer functions 41A30 Confluent hypergeometric functions 41A60 Computation of special functions Bessel functions Bessel function Polynomial Transcendental equation Numerical analysis Asymptotic expansion Recurrence relation Asymptotic behavior Hypergeometric function Asymptotic approximation Difference equation Numerical stability
ISSN:	0029-599X, 0945-3245
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