Help me take the derivative of the gamma function.

November 5, 2006 4:06 PM

How do I take the derivative of the gamma function, so I can prove that the derivative of the gamma function is the gamma function multiplied by the polygamma function?

So, I know the definition of both the gamma and polygamma functions (the integral definitions), and am trying to prove what I stated above. How do I do it? I just can't figure out how to get through the work.

posted by Loto to Science & Nature (4 answers total)

Best answer: This page on Mathworld (see equations 18-25) appears to have a proof.
posted by matthewr at 4:31 PM on November 5, 2006

Doesn't that proof say that gamma times the the first derivative of gamma is equal to gamma times polygamma?
posted by thisjax at 4:43 PM on November 5, 2006

Line 21 concludes that the derivative of gamma equals gamma multiplied by polygamma.
posted by matthewr at 4:48 PM on November 5, 2006

Response by poster: That is -perfect-, I ended up doing it a slightly different manner (to continue in the way I had started) but it is more or less the same.

Thank you muchly.
posted by Loto at 4:56 PM on November 5, 2006