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

Main Article Content

V. B. L. Chaurasia
R.C. Meghwal

Abstract

The aim of the present paper is to give unified presentation of certain families of elliptic-type integrals related to Euler integrals and generating functions. It is a unification and generalization of certain families of elliptic-type integrals which were studied in a number of earlier works on the subject due to their importance and potential in certain problems in radiation physics and nuclear technology. The results established in this paper are of manifold generality and basic in nature. Besides deriving various known and new elliptic-type integrals and their generalizations these theorems can be used to evaluate various Euler-type integrals involving a number of generating functions.

Article Details

How to Cite
Chaurasia, V. B. L., & Meghwal, R. (2012). Unified presentation of certain families of elliptic-type integrals related to Euler integrals and generating functions. Tamkang Journal of Mathematics, 43(4), 507–519. https://doi.org/10.5556/j.tkjm.43.2012.1320
Section
Papers
Author Biographies

V. B. L. Chaurasia, Department of Mathematics, University of Rajasthan

Department ofMathematics, University of Rajasthan, Jaipur-302055 (Rajasthan), India.

R.C. Meghwal, Department of Mathematics, Government Post-Graduate College

Department ofMathematics, Government Post-Graduate College, Neemuch-458441 (MP), India.

References

M. J. Berjer and J. C. Lankin, Sample calculation of gamma ray penetration into shelters. Contribution of sky shine and roof contamination, J. Res. N. B. S., 60(1958), 109--116.

J. Bjorkberg and G. Kristensson, Electromagnetic scattering by a perfectly conducting elliptic disc , Canad. J. Phys., 65(1987), 723--734.

P. F. Byrd and M. D. Friedman, Handbook of elliptic integrals for Engineers and Scientists, Springer, Berlin, 1971.

V. B. L. Chaurasia and S. C. Pandey, Unified elliptic-type integral and asymptotic formulas, Demonstratio Mathematica, 41(2008), 531--541.

L. F. Epstein and J. H. Hubbell, Evaluation of a generalized elliptic type integral, J. Res. N.B.S., 67(1963), 1--17.

J. D. Evans, J. H. Hubbell and V. D. Evans, Exact series solution to the Epstein-Hubbell generalized elliptic-type integral using complex variable residue theory}, Appl. Math. Comp., 53 (1993), 173--189.

M. L. Glasser and S. L. Kalla, Recursion relations for a class of generalized elliptic-type integrals, Rev. Tec. Ing. Univ. Zulia.,12 (1989), 47--50.

J. H. Hubbell, R. L. Bach and R. J. Herbold, Radiation field from a circular disk source, J. Res. N.B. S., 65 (1961), 249--264.

S. L. Kalla, Results on generalized elliptic-type integrals. Mathematical Structure-Computational mathematics-mathematical Modelling, 2, 216-219, Sofia: Publ. House Bulgar. Acad. Sci., 1984.

S. L. Kalla, The Hubbell rectangular source integral and its generalizations, Radiat. Phys. Chem., 41 (1993), 775--781.

S. L. Kalla, S. Conde and J. H. Hubbell, Some results on generalized elliptictype integrals}, Appl. Anal., 22 (1986), 273--287.

S. L. Kalla and B. Al-Saqabi, On a generalized elliptic-type integral, Rev. Bra. Fis.; 16(1986),145--156.

S. L. Kalla, C. Leubner and J. H. Hubbell, Further results on generalized Elliptic-type integrals, Appl. Anal., 25 (1987), 269--274.

S. L. Kalla and V. K. Tuan, Asymptotic formulas for generalized Elliptic-type integrals, Comput. Math. Appl., 32 (1996),49--55.

E. L. Kaplan, Multiple elliptic integrals, J. Math. And Phys., 29 (1950), 69--75.

S. S. Khadia and A. X. Goyal, On the generalized function ofn--variables, Vijnana Parishad Anusandhan Patrika, 13(1970), 191--201.

P. Kllinga and S. M. Khanna, Dose rate to the inner ear during Mosebauer experiments, Phys. Med. Biol., 28 (1983), 359--366.

B. N. Al-Saqabi, A generalization of elliptic-type integrals,Hadronic J., 10 (1987), 331--337.

A. Al-Zamel and V. K. Tuan, Kalla, S.L. Generalized Elliptic-type integrals and asymptotic formulas, Appl. Math. Comput., 114(2000), 13--25.

J. Matera L. Galue and S. L. Kalla, Asymptotic expansions for some elliptictype integrals, Raj. Acad. Phy. Sci., 1(2) (2002), 71--82.

A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and other Disciplines, New York, Halsted Press, 1978.

Ch. W. Mohammed, Bilinear and bilateral generating functions of generalized Polynomials, J. Austral. Math. Soc. Ser. B., 39 (1997), 257--270.

M. Salman, Generalized elliptic-type integrals and their representations, Appl. Math. Comput., 181(2) (2006), 1249--1256.

S. Saran, Theorems on bilinear generating functions, Indian J. Pure Appl. Math., 3(1972), 12--20.

R. K. Saxena and S. L. Kalla, Asymptotic formulas for unified Elliptic-type integrals, Int. Tran. Spec. Funct., 15 (4) (2004), 359--368.

R. K. Saxena, S. L. Kalla and J. H. Hubbell, Asymptotic expansion of a unified Elliptic-type integrals, Math. Balkanica, 15 (2001), 387--396.

R. K. Saxena and S. L. Kalla, A new method for evaluating Epstein--Hubbell generalized elliptic-type integrals, Int. J. Appl. Math.,2 (2000), 732--742.

R. K. Saxena and M. A. Pathan, Asymptotic formulas for unified elliptic-type integrals, Demonstratio Mathematica, 36 (3) (2003), 579--589.

R. N. Siddiqi, On a class of generalized elliptic-type integrals, Rev. Barsileira Fis., 19 (1989), 137--147.

H. M. Srivastava, Infinite series of certain products involving Appell's double hypergeometric functions I, Glasnik Mat., 4 (24) (1969), 67--73.

H. M. Srivastava and S. Bromberg, Some families of generalized elliptic-type integrals , Math. Comput. Modelling, 21(3)(1995), 29--38.

H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H--Functions of One and Two Variables with Applications, South Asian Publishers, New Delhi, 1982.

H. M. Srivastava and R. Panda, Some bilateral generating functions for a class of generalized hypergeometric polynomials, J. Reine Angew. Math., 283/284(1976), 265--274.

H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood Ltd., Chichester, 1985.

H. M. Srivastava and R. N. Siddiqi, A unified presentation of certain families of elliptic-type integrals related to radiation field problems, Radiant, Phy. Chem., 46 (1995), 303--315.

H. M. Srivastava and Y. N. Yeh, Certain theorems on bilinear and bilateral generating function}, ANZIAM J., 43 (2002), 567--574.