Problem in Gama function;can you answer soon.

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quantum220
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Hello i am very happy to sent my firest question,so i am very happy from forum.
my problem is : prove that
right&space;)^{m}2^{m}\sqrt{\pi&space;}}{1.3.5....\left&space;(&space;2m-1&space;\right&space;)}.gif

using
gif.gif



I try by:
let
gif.gif
 

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  • right&space;)^{m}2^{m}\sqrt{\pi&space;}}{1.3.5....\left&space;(&space;2m-1&space;\right&space;)}.gif
    right&space;)^{m}2^{m}\sqrt{\pi&space;}}{1.3.5....\left&space;(&space;2m-1&space;\right&space;)}.gif
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quantum220 said:
Hello i am very happy to sent my firest question,so i am very happy from forum.
my problem is :
prove that
right&space;)^{m}2^{m}\sqrt{\pi&space;}}{1.3.5....\left&space;(&space;2m-1&space;\right&space;)}.gif

The pi term comes from the fact that Gamma(1/2) = SQRT(pi). The rest you can deduce from using the relationship Gamma(x + 1) = x * Gamma(x). Basically because they are negative you are going to get switching signs since every step is multiplying by a negative number and the rest can be obtained from the definition. (I'm assuming m is an integer of course)