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1991-1992 | 56 | 1 | 19-28
Tytuł artykułu

Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We evaluate an integral involving an Hermite polynomial, a generalized hypergeometric series and Fox's H-function, and employ it to evaluate a double integral involving Hermite polynomials, generalized hypergeometric series and the H-function. We further utilize the integral to establish a Fourier-Hermite expansion and a double Fourier-Hermite expansion for products of generalized hypergeometric functions.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
56
Numer
1
Strony
19-28
Opis fizyczny
Daty
wydano
1991
otrzymano
1989-09-10
poprawiono
1990-06-01
Twórcy
  • V.B.R.I. Polytechnic, Vidya-Bhawan Rural Institute, Udaipur, India
Bibliografia
  • [1] S. D. Bajpai, An integral involving Fox's H-function and heat conduction, Math. Ed. (Siwan) 3 (1969), 1-4.
  • [2] S. D. Bajpai, An expansion formula for Meijer's G-function involving Hermite polynomials, Labdev J. Sci. Tech. Part A8 (1970), 9-11.
  • [3] B. R. Bhonsle, Heat conduction and Hermite polynomials, Proc. Nat. Acad. Sci. India Sect. A 36 (1966), 359-360.
  • [4] B. L. J. Braaksma, Asymptotic expansions and analytic continuations for a class of Barnes integrals, Compositio Math. 15 (1963), 239-341.
  • [5] A. Erdélyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York 1953.
  • [6] C. Fox, The G and H-functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429.
  • [7] G. K. Goyal, An integral involving H-function, Proc. Nat. Acad. Sci. India Sect. A 39 (1969), 201-203.
  • [8] K. C. Gupta and G. S. Olkha, Integrals involving the products of generalized hypergeometric functions and Fox's H-function, Univ. Nac. Tucumán Rev. Ser. A 19 (1969), 205-212.
  • [9] J. Kampé De Fériet, Heat conduction and Hermite polynomials, Bull. Calcutta Math. Soc., Golden Jubilee Commemoration Volume (1958-59), 103-104.
  • [10] A. M. Mathai and R. K. Saxena, Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Lecture Notes in Math. 348, Springer, Berlin 1973.
  • [11] A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, Wiley Eastern Ltd., New Delhi 1978.
  • [12] L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan, London 1933.
  • [13] E. D. Rainville, Special Functions, McGraw-Hill, New York 1960.
  • [14] M. Shah, On some results on the H-function involving Hermite polynomials, J. Natur. Sci. Math. 9 (1969), 223-233.
  • [15] M. Shah, Heat conduction, generalized Meijer's function and Hermite polynomials, Comment. Math. Univ. St. Paul. 19 (1970), 81-94.
  • [16] F. Singh and R. C. Varma, Application of E-operator to evaluate a definite integral and its application in heat conduction, J. Indian Math. Soc. (N.S.), 36 (1972), 325-332.
  • [17] H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-function of One and Two Variables with Applications, South Asian Publ., New Delhi 1982.
  • [18] J. Wimp and Y. L. Luke, Expansion formulae for generalized hypergeometric functions, Rend. Circ. Mat. Palermo 11 (1962), 351-366.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv56z1p19bwm
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