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Q: Problem with Mellin Barnes type integral

marioUsing the Mellin Barnes technique for a certain Feynman integral, I arrive at $$ I= \frac1{2\pi i} \int\limits_{-i\infty}^{i\infty} dz\; \Gamma^4\left(\frac12 + z\right) \Gamma^4\left(\frac12 - z\right) \psi\left(\frac12 - z\right)\,, $$ where $\psi(x)$ is the digamma-function. This i...

In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions. They were introduced by Ernest William Barnes (1908, 1910). They are closely related to generalized hypergeometric series. The integral is usually taken along a contour which is a deformation of the imaginary axis passing to the right of all poles of factors of the form Γ(a + s) and to the left of all poles of factors of the form Γ(a − s). == Hypergeometric series == The hypergeometric function is given as a Barnes integral (Barnes 1908) by...
 

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