Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion

DOI10.1016/S0377-0427(02)00608-8zbMath1026.65015MaRDI QIDQ1874159

Nico M. Temme, Amparo Gil, Javier Segura

Publication date: 22 May 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Bessel functionssteepest descent methodcontinued fraction methoduniform Airy-type asymptotic expansionsnonoscillatory integral representations

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 (5)

Computations of Green's Function and Its Fourier Coefficients on Fuchsian Groups ⋮ Maaß cusp forms for large eigenvalues ⋮ Unnamed Item ⋮ Summability experiments with a class of divergent inverse Kontorovich-Lebedev transforms ⋮ Bounds and algorithms for the -Bessel function of imaginary order

Cites Work

• Unnamed Item
• On the numerical evaluation of the modified Bessel function of the third kind
• Numerical algorithms for uniform Airy-type asymptotic expansions
• Evaluation of the modified Bessel function of the third kind of imaginary orders
• Computing complex Airy functions by numerical quadrature
• Steepest descent paths for integrals defining the modified Bessel functions of imaginary order
• Chebyshev Approximations for the Coulomb Phase Shift

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