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Volume :24 Issue : 2 1997      Add To Cart                                                                    Download

New results on the approximations of the generalised elliptic-type integrals

Auther : M. EL-GABALI

 Department of Mathematics and Computer Science, Kuwait University, P0 Box 5969,

Safat 13060 Kuwait e- mail: Gabaly@sci kuniv edu kw

(Note: Mathematical characters in this abstract could not be shown properly in html format. If you are interested in the full abstract, please send us an email message)

 ABSTRACT

The generalised elliptic-type integral R, cz, y)

(‘It iz—1 • 2y—2

where — (1 — k cos O) where 0 k < 1, Re(y) > Re( > 0, Re(y) > —0.5 has been represented in terms of the Gauss vr function by Kalla et al. (1986). Furthermore, Kalla et al. (1987) derived a simple-structured single term approximation for this function in the neighbourhood of k = 1 :n some range of the parameters , y and y. In this paper, a different technique is used to defi%e efficient two-term approximations in closed form in the neighbourhood of k = 1 for R z. y) which may be considered as an extension of the concept of the single term approximation mentioned above. Evidently, a closed form reduces computations considerably, and the improvement in accuracy by having two terms instead of a single one is manifested by the of the error from 0(h to 0(h where h = (1 — k 4 1. The technique used in the approximation may be interpreted as a rational approximation to a function that the two rational terms with four terms of the Taylor expansion. Results show that proposed technique is superior to existing approximations for the same number of terms. The formulation presented in this work has potential application for a wide class of special functions.

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