The Laplace transform of the product of three confluent hypergeometric functions is expressed in terms of Lauricella’s function FA(α,a1,a2,a3, b1,b2,b3; x,y,z). Two analytic continuation relations of the FA function are obtained by making use of its Barnes integral representation. One analytic continuation leads to a set of one term transformation relations and in the second, FA is expressed in terms of eight Lauricella FB series. Analytic continuations are given for the FB series, thereby allowing one to obtain a new analytic continuation for the FA series. Our result is useful for calculating the FA function when ‖x‖+‖y‖+‖z‖=2, which occurs in the analysis of the electron scattering from the nucleus.

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© 1978 American Institute of Physics.
1978
American Institute of Physics
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