EXPANSIONS FOR SOME CONFLUENT HYPERGEOMETRIC-FUNCTIONS

被引:11
|
作者
ABADIR, KM
机构
[1] Department of Economics, The American University in Cairo, Cairo
来源
关键词
D O I
10.1088/0305-4470/26/16/021
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Power series for the parabolic cylinder function, D(v)(z), are derived from known addition theorems, thus enabling a more compact and efficient expression of the function. One of the expansions is applied to find an asymptotic approximation for the function as absolute value of v --> infinity with \arg(-v)\ < pi. Next, a large-argument (z) asymptotic addition theorem is derived from an integral representation of D(v)(z). Before extending this type of summation theorem to the two general confluent hypergeometric functions, motivating mathematical applications to three integration problems are given as examples of the practical usefulness of the formulae.
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页码:4059 / 4066
页数:8
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