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converges for some complex value of *. It is then known that the integral will converge for all complex * of greater real part and will consequently define a function, which we have denoted by/(*), in a half-plane. By the inversion of the integral (1) we mean the determination of the function a(t) in terms of the function /(*). There is one special case of (1) of particular interest, that in which a(t) is a step-function with jumps only at the integral points. Then

The inversion of the Laplace integral and the related moment problem