Hypergeometric Series
The hypergeometric function is given as a Barnes integral (Barnes 1908) by
This equality can be obtained by moving the contour to the right while picking up the residues at s = 0, 1, 2, ... . Given proper convergence conditions, one can relate more general Barnes' integrals and generalized hypergeometric functions pFq in a similar way.
Read more about this topic: Barnes Integral
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