The Pochhammer contour is a specific type of contour used in complex analysis, particularly in the context of integrals involving certain types of functions or singularities. The contour is named after the mathematician Leo Pochhammer. The Pochhammer contour consists of a path in the complex plane that typically encloses one or more branch points, where a function may be multi-valued, such as logarithms or fractional powers.
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A commutator contour around two branch points cancels the total monodromy of its integrand. For the contour circling clockwise and then anticlockwise, with initial positive-real branches, the Beta function obeysThe contour integral is entire in , giving a meromorphic continuation of the Beta function.