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

Journal of Computational and Applied Mathematics

Volumn 153, Issue 1-2, 2003, Pages 225-234

  Gil, Amparo ^a   Segura, Javier ^b   Temme, Nico ^c  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^c CWI   (Netherlands)

Author keywords

Bessel functions; Nonoscillatory integral representations; Uniform Airy type asymptotic expansions

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; IMAGING TECHNIQUES; INTEGRAL EQUATIONS;

IMAGINARY ORDERS;

BESSEL FUNCTIONS;

MATHEMATICAL ANALYSIS;

EID: 0037381171     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00608-8     Document Type: Article

References (8)

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2. A. Gil, J. Segura, N.M. Temme, Evaluation of the modified Bessel functions of the third kind of imaginary orders, J. Comput. Phys. 17 (2002 398-411.
3. A. Gil, J. Segura, N.M. Temme, Computing complex Airy functions by numerical quadrature, Numer. Algorithms 30 (2002) 11-23.
4. F.J.W. Olver, Asymptotics and Special Functions, Reprinted in 1997 by AK Peters.
5. R. Piessens, E. De Doncker, Subroutine DQAGIE, obtained from SLATEC Public Domain Library.
6. N.M. Temme, On the numerical evaluation of the modified Bessel function of the third kind, J. Comput. Phys. 19 (3) (1975) 324-337.
7. N.M. Temme, Steepest descent paths for integrals defining the modified Bessel functions of imaginary order, Methods Appl. Anal. 1 (1994) 14-24.
8. N.M. Temme, Numerical algorithms for uniform Airy-type asymptotic expansions, Numer. Algorithms 15 (2) (1997) 207-225.