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Math Help - Gamma functions

  1. #1
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    Gamma functions

    Could somone help me to solve the following gamma function:

    T(2+i)/T(-2+i)

    Thank you
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  2. #2
    MHF Contributor chisigma's Avatar
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    May be You find useful the following expression of \Gamma(*) as 'infinite product'...

    \Gamma (z) = \frac {e^{-\gamma z}}{z} \prod_{n=1}^{\infty} \frac{e^{\frac{z}{n}}}{1+\frac{z}{n}}

    Kind regards

    \chi \sigma
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  3. #3
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    Use the recursion relation \Gamma(z+1)=z\Gamma(z). Then \frac{\Gamma(2+i)}{\Gamma(-2+i)}=\frac{i(1+i)(-1+i)(-2+i)\Gamma(i)}{\Gamma(i)}=2+4i.
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