Is there any relation between the limiting behaviour of $\Gamma({\epsilon})$ and $\Gamma(-1+{\epsilon})$? I have seen the relation such as $\Gamma(-1+{\epsilon})$ $=$ $\Gamma({\epsilon})/(-1+{\epsilon})$. I think it is basically wrong? But does there exist such a similar relation?
Gamma function of negative argument
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special-functions
gamma-function
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0In a small treatize on the Eulerian numbers I tried to make sense to the gamma-function at zero and negative integers including the aspect of epsilon-range deviations around the integer arguments at which the singularities occur. Perhaps this is giving some ideas to you.... see http://go.helms-net.de/math/binomial_new/01_12_Eulermatrix.pdf pg 8 ff – 2012-12-22
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0You may appreciate the discussion in this ['Limits defined for negative factorials'](http://math.stackexchange.com/questions/168223/limits-defined-for-negative-factorials-i-e-n-space-n-in-mathbbn) thread. – 2012-12-22