Computing the Conical Function $P^{\mu}_{-1/2+i\tau}(x)$

DOI10.1137/070712006zbMath1189.33006OpenAlexW1982740030MaRDI QIDQ3567003

Amparo Gil, Javier Segura, Nico M. Temme

Publication date: 10 June 2010

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/070712006

zbMATH Keywords

hypergeometric functionsmodified Bessel functionsdifference equationsasymptotic analysisLegendre functionsthree-term recurrence relationsnumerical evaluation of special functionsstability of recurrence relationsconical functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (4)

An improved algorithm and a Fortran 90 module for computing the conical function \(P^m_{-1/2+i\tau}(x)\) ⋮ The convolution for zero-order Mehler–Fock transform and pseudo-differential operator ⋮ A new \texttt{Fortran 90} program to compute regular and irregular associated Legendre functions ⋮ Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders

Uses Software

• Algorithm 831

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