Successive derivatives and finite expansions involving the H-function of one and more variables

C. M. Joshi; N. L. Joshi

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 1, page 15-29
  • ISSN: 0066-2216

Abstract

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Certain results including the successive derivatives of the H-function of one and more variables are established. These remove the limitations of Ławrynowicz's (1969) formulas and as a result extend the results of Skibiński [13] and various other authors. As an application some finite expansion formulas are also established, which reduce to hypergeometric functions of one and more variables that are of common interest.

How to cite

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C. M. Joshi, and N. L. Joshi. "Successive derivatives and finite expansions involving the H-function of one and more variables." Annales Polonici Mathematici 67.1 (1997): 15-29. <http://eudml.org/doc/270720>.

@article{C1997,
abstract = {Certain results including the successive derivatives of the H-function of one and more variables are established. These remove the limitations of Ławrynowicz's (1969) formulas and as a result extend the results of Skibiński [13] and various other authors. As an application some finite expansion formulas are also established, which reduce to hypergeometric functions of one and more variables that are of common interest.},
author = {C. M. Joshi, N. L. Joshi},
journal = {Annales Polonici Mathematici},
keywords = {H-function of several variables; differential operator; expansion formulas; Appell functions; Lauricella functions; Kampé de Fériet function; generalized hypergeometric functions},
language = {eng},
number = {1},
pages = {15-29},
title = {Successive derivatives and finite expansions involving the H-function of one and more variables},
url = {http://eudml.org/doc/270720},
volume = {67},
year = {1997},
}

TY - JOUR
AU - C. M. Joshi
AU - N. L. Joshi
TI - Successive derivatives and finite expansions involving the H-function of one and more variables
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 1
SP - 15
EP - 29
AB - Certain results including the successive derivatives of the H-function of one and more variables are established. These remove the limitations of Ławrynowicz's (1969) formulas and as a result extend the results of Skibiński [13] and various other authors. As an application some finite expansion formulas are also established, which reduce to hypergeometric functions of one and more variables that are of common interest.
LA - eng
KW - H-function of several variables; differential operator; expansion formulas; Appell functions; Lauricella functions; Kampé de Fériet function; generalized hypergeometric functions
UR - http://eudml.org/doc/270720
ER -

References

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  1. [1] P. Anandani, On the derivative of H-function, Rev. Roumaine Math. Pures Appl. 15 (1970), 189-191. Zbl0189.34403
  2. [2] J. L. Burchnall and T. W. Chaundy, On Appell's hypergeometric functions, Quart. J. Math. 11 (1940), 249-270. Zbl0025.16301
  3. [3] S. P. Goyal, The H-function of two variables, Kyungpook Math. J. 15 (1975), 117-131. Zbl0302.33004
  4. [4] K. C. Gupta and U. C. Jain, On the derivatives of H-function, Proc. Nat. Acad. Sci. India Sect. A 38 (1968), 189-192. Zbl0244.33012
  5. [5] R. N. Jain, General series involving H-function, Proc. Cambridge Philos. Soc. 65 (1969), 461-465. Zbl0169.08702
  6. [6] C. M. Joshi and N. L. Joshi, Reinvestigation of conditions of convergence of the H-function of two variables, submitted for publication. Zbl0878.33006
  7. [7] C. M. Joshi and M. L. Prajapat, On some results concerning generalized H-function of two variables, Indian J. Pure Appl. Math. 8 (1977), 103-116. Zbl0364.33007
  8. [8] J. Ławrynowicz, Remarks on the preceding paper of P. Anandani, Ann. Polon. Math. 21 (1969), 120-123. 
  9. [9] A. M. Mathai and R. K. Saxena, The H-function with Applications in Statistics and Other Disciplines, Wiley Eastern, New Delhi, 1978. Zbl0382.33001
  10. [10] M. L. Oliver and S. L. Kalla, On the derivative of Fox's H-function, Acta Mexican Ci. Tecn. 5 (1971), 3-5. 
  11. [11] R. K. Raina, On the repeated differentiation of H-function of two variables, Vijnana Parishad Anusandhan Patrika 21 (1978), 221-228. Zbl1195.33141
  12. [12] S. L. Rakesh, On the derivatives of the generalised Fox's H-function of two variables, Vijnana Parishad Anusandhan Patrika 18 (1975), 17-25. Zbl1195.33142
  13. [13] P. Skibiński, Some expansion theorems for the H-function, Ann. Polon. Math. 23 (1970), 125-138. Zbl0201.39001
  14. [14] L. F. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. Zbl0135.28101
  15. [15] H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Horwood, Chichester, 1985. Zbl0552.33001
  16. [16] H. M. Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables II, Comment. Math. Univ. St. Paul. 25 (1975), 169-197. 
  17. [17] H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-Functions of One and Two Variables with Applications, South Asian Publ., New Delhi-Madras, 1982. Zbl0506.33007

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