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

Annales Polonici Mathematici (1997)

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

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topC. 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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- [2] J. L. Burchnall and T. W. Chaundy, On Appell's hypergeometric functions, Quart. J. Math. 11 (1940), 249-270. Zbl0025.16301
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- [8] J. Ławrynowicz, Remarks on the preceding paper of P. Anandani, Ann. Polon. Math. 21 (1969), 120-123.
- [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] M. L. Oliver and S. L. Kalla, On the derivative of Fox's H-function, Acta Mexican Ci. Tecn. 5 (1971), 3-5.
- [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] 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] P. Skibiński, Some expansion theorems for the H-function, Ann. Polon. Math. 23 (1970), 125-138. Zbl0201.39001
- [14] L. F. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. Zbl0135.28101
- [15] H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Horwood, Chichester, 1985. Zbl0552.33001
- [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] 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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