- #1
touqra
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Has anyone seen this representation for gamma function before?
[tex]\Gamma(z) = \int_0^1\ dt\,\, t^{z-1}(e^{-t}\, -\, \sum_{n=0}^N\frac{(-t)^{n}}{n!})\,\, +\,\, \sum_{n=0}^N\frac{(-1)^{n}}{n!}\frac{1}{z+n}\,\, +\,\, \int_1^\infty dt\,\, e^{-t}\,t^{z-1}[/tex]
for Re(z) > -N-1
I can't figure out how to prove this...
[tex]\Gamma(z) = \int_0^1\ dt\,\, t^{z-1}(e^{-t}\, -\, \sum_{n=0}^N\frac{(-t)^{n}}{n!})\,\, +\,\, \sum_{n=0}^N\frac{(-1)^{n}}{n!}\frac{1}{z+n}\,\, +\,\, \int_1^\infty dt\,\, e^{-t}\,t^{z-1}[/tex]
for Re(z) > -N-1
I can't figure out how to prove this...
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