Unified Elliptic-Type Integrals and Asymptotic Formulas

Abstract

Abstract. The object of the present paper is to consider a unified and extended form of certain families of elliptic-type integrals, which have been discussed in number of earlier works on the subject due to their importance and applications in problems arising in radiation physics and nuclear technology. The results obtained are of general character and include the investigations carried out by several authors. We obtain asymptotic formulas for the unified elliptic-type integrals. IntroductionElliptic integrals occur in a number of physical problems [1-2], and frequently in the form of multiple integrals. For example, the problems dealing with the computation of the radiations field off axis from certain uniform circular 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:Elliptic integrals (1.1) have been studied and generalized by many authors notably by Kalla [5,6]

On certain generalized families of unified elliptic-type integrals pertaining to Euler integrals and generating functions

“…For σ → 0 and ω = sin 2 θ 2 with b i * = c i * ; a i * → 0, above (27) yields the following explicit representation of generalized family of the elliptic-type integral, recently investigated by Chaurasia and Pandey [4]. ...,λ N ,τ 1 ,...,τ M (ρ 1 ,... ,ρ N ,δ 1 ,... ,δ N ; k 1 …”

“…In a recent paper [4], we have proposed and investigated a new family of unified and generalized elliptic-type integrals:…”

Unified presentation of certain families of elliptic-type integrals related to Euler integrals and generating functions

“…In a recent paper [4], Chaurasia and Pandey investigated a new family of unified and generalized elliptic-type integrals:…”