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Generalized elliptic-type integrals and generating functions

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Języki publikacji
PL
Abstrakty
EN
On account of analytical importance or application in certain problems in radiation physics and nuclear technology, several interesting families of elliptic-type integrals were recently studied by many authors. The aim and objective of present paper is to obtain certain new theorems on generating functions. The results obtained in this paper are of manifold generality and basic in nature. In addition, to deriving known and various new elliptic-type integrals and their generalizations, these theorems can be used to evaluate various Euler-type integrals involving a number of generating functions.
Wydawca
Rocznik
Strony
310--323
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
  • Department of Mathematics, University of Rajasthan Jaipur-302004, Rajasthan, India
autor
  • Department of Mathematics, Jaipur National University Jagatpura, Jaipur-302025, Rajasthan, India
Bibliografia
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  • [3] J. D. Evans, J. H. Hubbell, V. D. Evans, Exact series solution to the Epstein-Hubbell generalized elliptic-type integral using complex variable residue theory, Appl. Math. Comput. 53 (1993), 173–189.
  • [4] J. H. Hubbell, R. L. Bach, R. J. Herbold, Radiataion field from a circular disk source, J. Res. N. B. S. 65 (1961), 249–264.
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  • [7] R. N. Siddiqi, On a class of generalized elliptic-type integrals, Rev. Bras. Fis. 19 (1989), 137–147.
  • [8] L. F. Epstein, J. H. Hubbell, Evaluation of a generalized elliptic-type integral, J. Res. N. B. S. 67 (1963), 1–17.
  • [9] S. L. Kalla, Results on generalized elliptic-type integrals, Mathematical structurecomputational mathematics-mathematical modelling 2, Publ. House Bulgar. Acad. Sci. Sofia, (1984), 216–219.
  • [10] S. L. Kalla, The Hubbell rectangular source integral and its generalizations, Radiat. Phys. Chem. 41 (1993), 775–781.
  • [11] S. L. Kalla, S. Conde, J. H. Hubbell, Some results on generalized elliptic-type integrals, Appl. Anal. 22 (1986), 273–287.
  • [12] S. L, Kalla, B. Al-Saqabi, On a generalized elliptic-type integral, Rev. Bras. Fis. 16 (1986), 145–156.
  • [13] S. L. Kalla, C. Leubner, J. H. Hubbell, Further results on generalized elliptic-type integrals, Appl. Anal. 25 (1987), 269–274.
  • [14] M. Salman, Generalized elliptic-type integrals and their representations, Appl. Math. Comput. 181(2) (2006), 1249–1256.
  • [15] R. K. Saxena, S. L. Kalla, J. H. Hubbell, Asymptotic expansion of a unified elliptic-type integrals, Math. Balkanica (N.S.) 15 (2001), 387–396.
  • [16] H. M. Srivastava, S. Bromberg, Some families of generalized elliptic-type integrals, Math. Comput. Modelling 21(3) (1995), 29–38.
  • [17] M. L. Glasser, S. L. Kalla, Recursion relations for a class of generalized elliptic-type integrals, Rev. Tecn. Fac. Ingr. Univ. Zulia 12 (1989), 47–50.
  • [18] B. N. Al-Saqabi, A generalization of elliptic-type integrals, Hadronic J. 10 (1987), 331–337.
  • [19] J. Matera, L. Galue, S. L. Kalla, Asymptotic expansions for some elliptic-type integrals, J. Rajasthan Acad. Phys. Sci. 1(2) (2002), 71–82.
  • [20] H. M. Srivastava, R. N. Siddiqi, A unified presentation of certain families of elliptic-type integrals related to radiation field problems, Radiat. Phys. Chem. 46 (1995), 303–315.
  • [21] S. L. Kalla, V. K. Tuan, Asymptotic formulas for generalized elliptic-type integrals, Comput. Math. Appl. 32 (1996), 49–55.
  • [22] R. K. Saxena, S. L. Kalla, A new method for evaluating Epstein-Hubbell generalized elliptic-type integrals, Int. J. Appl. Math. 2 (2000), 732–742.
  • [23] R. K. Saxena, A. M. Pathan, Asymptotic formulas for unified elliptic-type integrals, Demonstratio Math. 36(3) (2003), 579–589.
  • [24] V. B. L. Chaurasia, S. C. Pandey, Unified elliptic-type integrals and asymptotic formulas, Demonstratio Math. 41(3) (2008), 531–541.
  • [25] R. K. Saxena, S. L. Kalla, Asymptotic formulas for unified elliptic-type integrals, Integral Transforms Spec. Funct. 15(4) (2004), 359–368.
  • [26] V. P. Saxena, A formal solution of certain new pair of dual integral equation involving H-functions, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. 52 (1982), 366–375.
  • [27] W. Ch. Mohammed, Bilinear and bilateral generating functions of generalized polynomials, J. Aust. Math. Soc. Ser. B 39 (1997), 257–270.
  • [28] S. Saran, Theorems on bilinear generating functions, Indian J. Pure Appl. Math. 3 (1972), 12–20.
  • [29] H. M. Srivastava, Y. N. Yeh, Certain theorem on bilinear and bilateral generating functions, ANZIAM J. 43 (2000), 567–574.
  • [30] H. M. Srivastava, H. L. Manocha, A Treatise on Generating Functions, Chichester, Ellis Horwood Ltd. (1985).
  • [31] V. B. L. Chaurasia, S. C. Pandey, On certain generalized families of unified elliptictype integrals pertaining to Euler integrals and generating functions, Rend. Circ. Mat. Palermo (2) 58 (2009), 69–86.
  • [32] V. B. L. Chaurasia, R. C. Meghwal, Unified presentation of certain families of elliptic-type integrals related to Euler integrals and generating functions, Tamkang J. Math. 43(4) (2012), 507–519.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fad7bc53-b5ee-4f30-905e-74b430b91517
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