Result: A regularization technique for computing the hypergeometric function \(F(a,b;c;z)\)in the neighborhood of the singular points \(z=1\) and \(z= \infty\)

Title:
A regularization technique for computing the hypergeometric function \(F(a,b;c;z)\)in the neighborhood of the singular points \(z=1\) and \(z= \infty\)
Authors:
Skorokhodov, S. L.
Publisher Information:
Springer US, New York, NY; Pleiades Publishing, New York, NY; MAIK ``Nauka/Interperiodica'', Moscow
Subject Terms:
Classical hypergeometric functions, \({}_2F_1\), Computation of special functions and constants, construction of tables, computing, accuracy, efficiency, Gauss hypergeometric function, pole, Numerical approximation and evaluation of special functions, singular points, regularization method
Document Type:
Academic journal Article
File Description:
application/xml
Access URL:
https://zbmath.org/1940565
Accession Number:
edsair.c2b0b933574d..bf1a9e9e945c7de9e0d234a65e1bb567
Database:
OpenAIRE

Further Information

In this paper the author suggests a new technique for the computation of the Gauss hypergeometric function \(F(a,b;c;z)\) in the neighborhood of the singular points \(z=1\) and \(z=\infty\) for the values of the complex parameters \(a,b,\) and \(c\) in the vicinity of the poles. In order to avoid operations with very large numbers and the corresponding loss of accuracy in the calculation a new regularization method is proposed. Ref. 20 in number.