Journal article
Computing the real zeros of hypergeometric functions



Publication Details
Authors:
Gil, A.; Koepf, W.; Segura, J.
Publication year:
2004
Journal:
Numerical Algorithms
Pages range:
113-134
Volume number:
36
Start page:
113
End page:
134
ISSN:
1017-1398

Abstract
Efficient methods for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. These methods are based on global fixed point iterations which apply to families of functions satisfying first order linear difference differential equations with continuous coefficients. In order to compute the zeros of arbitrary solutions of the hypergeometric equations, we have at our disposal several different sets of difference differential equations (DDE). We analyze the behavior of these different sets regarding the rate of convergence of the associated fixed point iteration. It is shown how combinations of different sets of DDEs, depending on the range of parameters and the dependent variable, is able to produce efficient methods for the computation of zeros with a fairly uniform convergence rate for each zero.


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Last updated on 2019-01-11 at 16:04