Some analytic or asymptotic confluent expansions for functions of several variables

Authors:
H. M. Srivastava and Rekha Panda

Journal:
Math. Comp. **29** (1975), 1115-1128

MSC:
Primary 33A65

MathSciNet review:
0387695

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Abstract: This paper aims at presenting multivariable extensions of the recent results of J. L. Fields [5] and others (cf. [1]-[4]) on certain analytic or asymptotic confluent expansions for functions of one and two variables. It is also demonstrated how these extensions would apply, for instance, to derive an asymptotic confluent expansion for a certain class of the generalized Lauricella function of several variables.

**[1]**V. M. Bhise and V. L. Deshpande,*On asymptotic confluent expansions for functions of two variables*, Nederl. Akad. Wetensch. Proc. Ser. A 75=Indag. Math.**34**(1972), 106–112. MR**0330526****[2]**V. L. Deshpande,*Theorems involving confluent asymptotic expansions of functions of two variables*, An. Univ. Timişoara Ser. Şti. Mat.**8**(1970), 143–151 (English, with Romanian summary). MR**0326029****[3]**V. L. Deshpande,*Confluent asymptotic expansions for functions of two variables*, Mat. Vesnik**10(25)**(1973), 221–226. MR**0335862****[4]**V. L. Deshpande,*Confluent expansions for functions of two variables*, Math. Comp.**28**(1974), 605–611. MR**0340657**, 10.1090/S0025-5718-1974-0340657-X**[5]**Jerry L. Fields,*Confluent expansions*, Math. Comp.**21**(1967), 189–197. MR**0224880**, 10.1090/S0025-5718-1967-0224880-7**[6]**Yudell L. Luke,*The special functions and their approximations, Vol. I*, Mathematics in Science and Engineering, Vol. 53, Academic Press, New York-London, 1969. MR**0241700****[7]**H. M. Srivastava and Martha C. Daoust,*Certain generalized Neumann expansions associated with the Kampé de Fériet function*, Nederl. Akad. Wetensch. Proc. Ser. A 72 = Indag. Math.**31**(1969), 449–457. MR**0252701****[8]**H. M. Srivastava and Martha C. Daoust,*A note on the convergence of Kampé de Fériet’s double hypergeometric series*, Math. Nachr.**53**(1972), 151–159. MR**0316763**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0387695-X

Keywords:
Analytic confluent expansion,
asymptotic confluent expansion,
generalized Lauricella functions,
generalized Bernoulli polynomials and numbers,
Vandermonde's theorem,
Poincaré coefficients,
confluent hypergeometric function

Article copyright:
© Copyright 1975
American Mathematical Society