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Tau method approximation of a generalized Epstein-Hubbell elliptic-type integral. (English) Zbl 0930.33007

In the present work, the author considers a generalization of the Epstein-Hubbell elliptic-type integral introduced by S. L. Kalla and V. K. Tuan in a previous paper [Comput. Math. Appl. 32, No. 4, 49-55 (1996; Zbl 0891.33010)]. In this respect, he uses the tau method [see C. Lanczos, Applied Analysis (1961; Zbl 0111.12403)] to obtain polynomial approximations to this integral for suitable values of some of its parameters.

MSC:

33C65 Appell, Horn and Lauricella functions
41A10 Approximation by polynomials
65D20 Computation of special functions and constants, construction of tables

Software:

Mathematica
Full Text: DOI

References:

[1] A. Al-Zamel and S. Kalla, Epstein-Hubbell elliptictype integral and its generalizations, Appl. Math. Comput. 77 (1996), no. 1, 9 – 32. · Zbl 0845.33011 · doi:10.1016/0096-3003(95)00147-6
[2] Leo F. Epstein and J. H. Hubbell, Evaluation of a generalized elliptic-type integral, J. Res. Nat. Bur. Standards Sect. B 67B (1963), 1 – 17. · Zbl 0114.06402
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[8] S.L. Kalla and V.K. Tuan. Asymptotic formulas for generalized elliptic-type integrals. In Proc. of the Intl. Wkshp. on Recent Advances in Applied Maths., Kuwait, 1996. Kuwait Univ. - KFAS. · Zbl 0891.33010
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[10] C. Lanczos. Applied Analysis. Prentice-Hall, New Jersey, 1956. · Zbl 0111.12403
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