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Simplify $\dfrac{2a\cdot\Gamma(2a)}{\Gamma(2a+1)}$.

Where $a$ is any positive real number.

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Is $a$ a natural number? – m0nhawk Jun 9 '14 at 8:42
@some1, no a is positive real – SA-255525 Jun 9 '14 at 8:43
up vote 4 down vote accepted

It's pretty simple. Check Gamma function definition for help. Or look into spoilers for solution.

Actually, this requires only one equation related to Gamma function: $$\Gamma(1 + z) = z\Gamma(z)$$ So, the expression equals to $1$.

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thanks for your help.your answer confirmed some of my results. – SA-255525 Jun 9 '14 at 10:28

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