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

Sadhana Mishra

Annales Polonici Mathematici (1991)

  • Volume: 56, Issue: 1, page 19-28
  • ISSN: 0066-2216

Abstract

top
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.

How to cite

top

Sadhana Mishra. "Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions." Annales Polonici Mathematici 56.1 (1991): 19-28. <http://eudml.org/doc/262365>.

@article{SadhanaMishra1991,
abstract = {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.},
author = {Sadhana Mishra},
journal = {Annales Polonici Mathematici},
keywords = {Fox -function; Hermite polynomial; generalized hypergeometric series},
language = {eng},
number = {1},
pages = {19-28},
title = {Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions},
url = {http://eudml.org/doc/262365},
volume = {56},
year = {1991},
}

TY - JOUR
AU - Sadhana Mishra
TI - Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions
JO - Annales Polonici Mathematici
PY - 1991
VL - 56
IS - 1
SP - 19
EP - 28
AB - 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.
LA - eng
KW - Fox -function; Hermite polynomial; generalized hypergeometric series
UR - http://eudml.org/doc/262365
ER -

References

top
  1. [1] S. D. Bajpai, An integral involving Fox's H-function and heat conduction, Math. Ed. (Siwan) 3 (1969), 1-4. Zbl0174.10602
  2. [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. [3] B. R. Bhonsle, Heat conduction and Hermite polynomials, Proc. Nat. Acad. Sci. India Sect. A 36 (1966), 359-360. Zbl0227.35053
  4. [4] B. L. J. Braaksma, Asymptotic expansions and analytic continuations for a class of Barnes integrals, Compositio Math. 15 (1963), 239-341. Zbl0129.28604
  5. [5] A. Erdélyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York 1953. Zbl0051.30303
  6. [6] C. Fox, The G and H-functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429. Zbl0096.30804
  7. [7] G. K. Goyal, An integral involving H-function, Proc. Nat. Acad. Sci. India Sect. A 39 (1969), 201-203. Zbl0244.33011
  8. [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. Zbl0185.29801
  9. [9] J. Kampé De Fériet, Heat conduction and Hermite polynomials, Bull. Calcutta Math. Soc., Golden Jubilee Commemoration Volume (1958-59), 103-104. 
  10. [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. Zbl0272.33001
  11. [11] A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, Wiley Eastern Ltd., New Delhi 1978. Zbl0382.33001
  12. [12] L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan, London 1933. Zbl59.1111.01
  13. [13] E. D. Rainville, Special Functions, McGraw-Hill, New York 1960. Zbl0092.06503
  14. [14] M. Shah, On some results on the H-function involving Hermite polynomials, J. Natur. Sci. Math. 9 (1969), 223-233. Zbl0195.06602
  15. [15] M. Shah, Heat conduction, generalized Meijer's function and Hermite polynomials, Comment. Math. Univ. St. Paul. 19 (1970), 81-94. Zbl0202.05504
  16. [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. Zbl0268.33007
  17. [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. Zbl0506.33007
  18. [18] J. Wimp and Y. L. Luke, Expansion formulae for generalized hypergeometric functions, Rend. Circ. Mat. Palermo 11 (1962), 351-366. Zbl0144.06902

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.