The Region of Convergence of the Complex Inversion Integral with Angular Path. The Holomorphy of the Represented Function
We now admit singularities of F(s) to the left of a which are not all single-valued. In the case that the first encountered singularities to the left of a are single-valued, one can employ the previous method and thus separate from f(t) the corresponding residues, until one finally encounters a many-valued singularity. Thus, we may, without loss of generality, assume that in the first encountered singular point to the left of a, that is the singular point α 0 with largest real part < a, F(s) has a many-valued singularity, perhaps of the character (s − α 0 )1/2 or (s − α0)−1/2 or log (s − α0) or (s − α 0 )1/2 log (s − α 0 ) etc. Possibly, one may encounter more than one singular point with identical largest real part < a; this particular situation will be discussed at the end of this Chapter.
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