Computing the complex zeros of special functions

DOI10.1007/S00211-013-0528-6zbMath1271.65087OpenAlexW2088755567MaRDI QIDQ2391811

Javier Segura

Publication date: 5 August 2013

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-013-0528-6

zbMATH Keywords

numerical examplesBessel functionsparabolic cylinder functionsgeneralized Bessel polynomialsLiouville-Green (WKB) approximationanti-Stokes linescomplex zeros of solutionsforuth-order method

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of solutions to single equations (65H05) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical approximation and evaluation of special functions (33F05) Oscillation, growth of solutions to ordinary differential equations in the complex domain (34M10)

Related Items (3)

Bessel phase functions: calculation and application ⋮ On the complex zeros of Airy and Bessel functions and those of their derivatives ⋮ Rate of approximation of \(z f^\prime (z)\) by special sums associated with the zeros of the Bessel polynomials

Uses Software

• DLMF

Cites Work

• Accurate computation of the zeros of the generalized Bessel polynomials
• Reliable Computation of the Zeros of Solutions of Second Order Linear ODEs Using a Fourth Order Method
• Physical Problems Solved by the Phase-Integral Method
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
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