Expansions for some confluent hypergeometric functions

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Abstract
Power series for the parabolic cylinder function, Dv(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 mod v mod to infinity with mod arg(-v) mod ( pi . Next, a large-argument (z) asymptotic addition theorem is derived from an integral representation of Dv(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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