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paco_uk
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Homework Statement
Starting from the Gamma function:
[tex]
\Gamma (s) = \int^{\infty}_{0} dx \, x^{s-1} e^{-x}
[/tex]
Make a change of variable to express it in the form:
[tex]
\Gamma (s) = f(s) \int^{\infty}_{0} dy \, \exp{\frac{-A(y)}{\zeta(s)}}
[/tex]And identify the functions f(s), A(y), [tex]\zeta[/tex](s).
Homework Equations
The Attempt at a Solution
I've tried various solutions along the lines of [tex]x^{s}[/tex] and [tex] e^y [/tex] but I can't find anything that works and I don't know any general methods for finding an appropriate substitution. Can anyone suggest where to start?
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