Analytical and numerical aspects of a generalization of the complementary error function

Applied Mathematics and Computation

Volumn 216, Issue 12, 2010, Pages 3680-3693

  Deaño, Alfredo ^a   Temme, Nico M ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b CWI   (Netherlands)

Author keywords

Asymptotic expansions; Complementary error function; Confluent hypergeometric function; Incomplete gamma function; Recurrence relations; Singular perturbation problem

Indexed keywords

ASYMPTOTIC EXPANSION; CONFLUENT HYPERGEOMETRIC FUNCTIONS; ERROR FUNCTION; INCOMPLETE GAMMA FUNCTIONS; RECURRENCE RELATIONS; SINGULAR PERTURBATION PROBLEMS;

EXPANSION; NUMERICAL METHODS;

ASYMPTOTIC ANALYSIS;

EID: 77953613086     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.05.025     Document Type: Article

References (13)

1. Milton Abramowitz, Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964.
2. Ciarkowski A. Uniform and quasi-uniform asymptotic expansions of incomplete diffraction integrals. SIAM J. Appl. Math. 48 6 (1988) 1217-1226
3. Ciarkowski A. Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point. Proc. Roy. Soc. London Ser. A 426 1871 (1989) 273-286
4. Deaño A., Segura J., and Temme N.M. Identifying minimal and dominant solutions for Kummer recursions. Math. Comput. 77 (2007) 2277-2293
5. Deaño A., and Temme N.M. On modified asymptotic series involving confluent hypergeometric functions. Electron. Trans. Numer. Anal. 35 (2009) 88-103
6. Gil A., Segura J., and Temme N.M. Numerical Methods for Special Functions (2007), SIAM, Philadelphia, PA
7. Jones D.S. The generalized Goodwin-Staton integral. Proc. Edinburgh Math. Soc., 2 48 3 (2005) 635-650
8. López J.L., and Sinusi{dotless}́a E.P. The role of the error function in a singularly perturbed convection-diffusion problem in a rectangle with corner singularities. Proc. Roy. Soc. Edinburgh Sect. A 137 1 (2007) 93-109
9. López J.L., Sinusi{dotless}́a E.P., and Temme N.M. First order approximation of an elliptic 3D singular perturbation problem. Stud. Appl. Math. 116 3 (2006) 303-319
10. Mamedov B.A. Evaluation of the generalized Goodwin-Staton integral using binomial expansion theorem. J. Quant. Spect. Rad. Transfer 105 (2007) 8-11
11. Frank W.J. Olver, Asymptotics and Special Functions, AKP Classics, AK Peters Ltd., Wellesley, MA, 1997, Reprint of the 1974 original [Academic Press, New York; MR 55 #8655].
12. Temme N.M. Special Functions: An Introduction to the Classical Functions of Mathematical Physics (1996), A Wiley-Interscience Publication, John Wiley & Sons Inc., New York
13. R. Wong. Asymptotic approximations of integrals, Classics in Applied Mathematics, vol. 34, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2001, Corrected reprint of the 1989 original.