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DEMONSTRATIO MATHEMATICAVol. XLINo 32008V. B. L. Chaurasia, S.C. PandeyUNIFIED E L L I P T I C - T Y P E INTEGRALS ANDASYMPTOTIC FORMULASA b s t r a c t . The object of the present paper is to consider a unified and extendedform of certain families of elliptic-type integrals, which have been discussed in number ofearlier works on the subject due to their importance and applications in problems arisingin radiation physics and nuclear technology. The results obtained are of general characterand include the investigations carried out by several authors. We obtain asymptoticformulas for the unified elliptic-type integrals.1. IntroductionElliptic integrals occur in a number of physical problems [1-2], and frequently in the form of multiple integrals. For example, the problems dealingwith the computation of the radiations field off axis from certain uniformcircular disc radiating according to an arbitrary angular distribution law [3],when treated with Legendre polynomials expansion method, give rise to Epstein and Hubbell [4, 21] family of elliptic-type integrals:7r(1.1)f2j(k)= \(l-k2cosdyj-%od6-,j = 0,1,2,...and 0 < k < 1.Elliptic integrals (1.1) have been studied and generalized by many authors notably by Kalla [5, 6] and Kalla et al. [7]. Kalla and Al-Saqabi [8]and Saxena et al. [9], Kalla
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 2008
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