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Thanks to sound remarks here and here, and looking again at these equations, I noticed that my puzzle boils down to these 2 special functions: $ $ \int_0^x I_i(u) e^{-a u}du, \quad i=0,1$ $ where $ I_n(u)$ is the modified Bessel of the first kind. Are these integral echoing something known in the literature? WhatRead more