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1997 | 67 | 1 | 15-29
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Successive derivatives and finite expansions involving the H-function of one and more variables

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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.
  • Department of Mathematics and Statistics, M. L. Sukhadia University, Udaipur 313001, India
  • S. M. B. Government College, Nathadwara, Rajasthan, India
  • [1] P. Anandani, On the derivative of H-function, Rev. Roumaine Math. Pures Appl. 15 (1970), 189-191.
  • [2] J. L. Burchnall and T. W. Chaundy, On Appell's hypergeometric functions, Quart. J. Math. 11 (1940), 249-270.
  • [3] S. P. Goyal, The H-function of two variables, Kyungpook Math. J. 15 (1975), 117-131.
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  • [8] J. Ławrynowicz, Remarks on the preceding paper of P. Anandani, Ann. Polon. Math. 21 (1969), 120-123.
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  • [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.
  • [13] P. Skibiński, Some expansion theorems for the H-function, Ann. Polon. Math. 23 (1970), 125-138.
  • [14] L. F. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966.
  • [15] H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Horwood, Chichester, 1985.
  • [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.
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