Computing special functions by using quadrature rules

Numerical Algorithms

Volumn 33, Issue 1-4, 2003, Pages 265-275

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

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b UNIVERSITY OF CANTABRIA   (Spain)

^c CWI   (Netherlands)

Author keywords

Airy functions; Bessel functions; Numerical computation of special functions; Numerical quadrature; Saddle point method; Steepest descent method

Indexed keywords

EID: 0041375523     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025524324969     Document Type: Conference Paper

References (15)

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7. A. Gil, J. Segura and N.M. Temme, Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion, J. Comput. Appl. Math. (2001) accepted.
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9. A. Gil, J. Segura and N.M. Temme, GIZ, HIZ: Two Fortran 77 routines for the computation of complex Scorer functions, ACM Trans. Math. Software 28 (2002) 436-447.
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11. A. Gil, J. Segura and N.M. Temme, Integral representations for computing real parabolic cylinder functions (2002) submitted.
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13. Y.L. Luke, The Special Functions and Their Approximations, Vols. I, II (Academic Press, New York, 1969).
14. N.M. Temme, Steepest descent paths for integrals defining the modified Bessel functions of imaginary order, Methods Appl. Anal. 1 (1994) 14-24.
15. N.M. Temme, Special Functions: An Introduction to the Classical Functions of Mathematical Physics (Wiley, New York, 1996).