Computing special functions by using quadrature rules

DOI10.1023/A:1025524324969zbMath1031.65033MaRDI QIDQ1410477

Javier Segura, Amparo Gil, Nico M. Temme

Publication date: 14 October 2003

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

algorithmsnumerical quadraturespecial functionsBessel functionsintegral representationssaddle point methodsteepest descent methodAiry functionsparabolic cylinder functions

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical approximation and evaluation of special functions (33F05)

Related Items (7)

A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line ⋮ Theory and numerical evaluation of oddoids and evenoids: oscillatory cuspoid integrals with odd and even polynomial phase functions ⋮ Spherical Bessel transform via exponential sum approximation of spherical Bessel function ⋮ Talbot quadratures and rational approximations ⋮ Zeros of the Macdonald function of complex order ⋮ Fast and accurate computation of Bessel functions with (large) complex order and argument ⋮ Numerical quadrature computation of the Macdonald function for complex orders

Uses Software

• AIZ
• BIZ
• Algorithm 644
• Algorithm 822

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