Abstract
We study the Kampé de Fériet double series \( F_{1:1;1}^{1:1;1 } \) through the solution to the associated first-order nonhomogeneous differential equation. We show that the integral of t β+l M(⋅; β; λt)M(⋅; β;−λt) over t ∈ [0, T], T ⩾ 0, \( l=0,1,\ldots,\Re \beta +l>-1 \), is a linear combination of functions \( F_{1:1;1}^{1:1;1 } \). The integral is a generalization of a class of the so-called Coulomb integrals involving regular Coulomb wave functions.
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Juršėnas, R. On the definite integral of two confluent hypergeometric functions related to the Kampé de Fériet double series. Lith Math J 54, 61–73 (2014). https://doi.org/10.1007/s10986-014-9227-y
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DOI: https://doi.org/10.1007/s10986-014-9227-y