Generalized Elliptic-Type Integrals and Generating Functions
نویسندگان
چکیده
منابع مشابه
Generalized elliptic-type integrals and asymptotic formulas
A number of families of elliptic-type integrals have been studied recently due to their importance and potential for applications in some problems of radiation physics. The object of this work is to present a unified and generalized form of such elliptic-type integrals and to study its properties, including recurrence formulas and asymptotic expansion.
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Epstein-Hubbell [6] elliptic-type integrals occur in radiation field problems. The object of the present paper is to consider a unified form of different elliptic-type integrals, defined and developed recently by several authors. We obtain asymptotic formulas for the generalized elliptic-type integrals. Keywords—Elliptic-type Integrals, Hypergeometric Functions, Asymptotic Formulas.
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In geometric function theory, generalized elliptic integrals and functions arise from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan’s modular equations and approximations to π. The authors stu...
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As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9 to 19 obtained by truncating Taylor series exp...
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ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2014
ISSN: 2391-4661,0420-1213
DOI: 10.2478/dema-2014-0025