Some analytic or asymptotic confluent expansions for functions of several variables

Srivastava, H. M.; Panda, Rekha

doi:10.1090/S0025-5718-1975-0387695-X

Some analytic or asymptotic confluent expansions for functions of several variables
HTML articles powered by AMS MathViewer

by H. M. Srivastava and Rekha Panda PDF

Math. Comp. 29 (1975), 1115-1128 Request permission

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.

References

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
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 326029
V. L. Deshpande, Confluent asymptotic expansions for functions of two variables, Mat. Vesnik 10(25) (1973), 221–226. MR 335862
V. L. Deshpande, Confluent expansions for functions of two variables, Math. Comp. 28 (1974), 605–611. MR 340657, DOI 10.1090/S0025-5718-1974-0340657-X
Jerry L. Fields, Confluent expansions, Math. Comp. 21 (1967), 189–197. MR 224880, DOI 10.1090/S0025-5718-1967-0224880-7
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
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
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 316763, DOI 10.1002/mana.19720530114