Uniform asymptotic expansions of symmetric elliptic integrals

Constructive Approximation

Volumn 17, Issue 4, 2001, Pages 535-559

  Lopez J L ^a  

^a PUBLIC UNIVERSITY OF NAVARRE   (Spain)

Author keywords

Distributional approach; Elliptic integrals; Uniform asymptotic expansions

Indexed keywords

EID: 0035648223     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003650010038     Document Type: Article

References (18)

1. M. ABRAMOWITZ, I. A. STEGUN ( 1970): Handbook of Mathematical Functions. New York: Dover.
2. P. F. BYRD, M. D. FRIEDMAN (1971): Handbook of Elliptic Integrals for Engineers and Scientists. New York: Springer-Verlag.
3. B. C. CARLSON (1985): The hypergeometric function and the R-function near their branch points. Rend. Sem. Math. Univ. Politec. Torino, Fascicolo speciale, pp. 63-89.
4. B. C. CARLSON, J. L. GUSTAFSON (1985): Asymptotic expansion of the first elliptic integral. SIAM J. Math. Anal., 16:1072-1092.
5. B. C. CARLSON (1987): A table of elliptic integrals of the second kind. Math. Comp., 49:595-606.
6. B. C. CARLSON (1988): A table of elliptic integrals of the third kind. Math. Comp., 51:267-280.
7. B.C. CARLSON (1989): A table of elliptic integrals: Cubic cases. Math. Comp., 53:327-333.
8. B. C. CARLSON (1991): A table of elliptic integrals: One quadratic factor. Math. Comp., 56:267-280.
9. B. C. CARLSON (1992): A table of elliptic integrals: Two quadratic factors. Math. Comp., 59:165-180.
10. B. C. CARLSON, J. L. GUSTAFSON (1994): Asymptotic approximations for symmetric elliptic integrals. SIAM J. Math. Anal., 25:288-303.
11. J. L. GUSTAFSON (1982): Asymptotic formulas for elliptic integrals. Ph.D. Thesis. Ames. IA: Iowa State University.
12. E. L. KAPLAN (1948): Auxiliary table for the incomplete elliptic integrals. J. Math. Phys., 27:11-36.
13. A. M. LEGENDRE (1825): Traité des Fonctions Elliptiques, Vol. I. Paris: Imprimerie de Huzard-Courcier.
14. J. L. LÓPEZ (2000): Asymptotic expansions of symmetric standard elliptic integrals. SIAM J. Math. Anal., 31(4):754-775.
15. A. P. PRUDNIKOV, YU. A. BRYCHKOV, O. I. MARICHEV (1990): Integrals and Series, Vol. 1. New York: Gordon and Breach.
16. N. M. TEMME (1996): Special Functions: An Introduction to the Classical Functions of Mathematical Physics. New York: Wiley.
17. R. WONG ( 1979): Explicit error terms for asymptotic expansions of Mellin convolutions. J. Math. Anal. Appl., 72:740-756.
18. R. WONG (1989): Asymptotic Approximations of Integrals. New York: Academic Press.