Talk:Polygamma function

Particular values
A list of particular values would be useful. It seems that $$\psi (0,1/2)= -\gamma - \ln(4)$$ for example, where $$\gamma$$ is the Euler–Mascheroni constant. PAR (talk) 00:49, 27 May 2011 (UTC)

Colours in graphs
The article includes six graphs of the (poly)gamma function, very attractively coloured throughout a rectangular region of the complex plane. However, there is absolutely no explanation of the colours used! What do they mean?

Note that the digamma function page has a similar problem. yoyo (talk) 05:09, 27 June 2015 (UTC)
 * See color wheel graphs of complex functions. Double sharp (talk) 09:31, 24 September 2015 (UTC)

Notability: derivatives of the gamma function
The polygamma function is a very important and significant function in pure mathematics, and surely it satisfies Wikipedia's general notability guideline!

The polygamma functions are the derivatives of the logarithm of the gamma function, and this is the standard method to calculate the derivative of the gamma function in general. For example, in the Wikipedia article on the gamma function itself, it is stated, "The derivatives of the gamma function are described in terms of the polygamma function."

The gamma function is one of the most important, significant, and fundamental functions in all of pure mathematics. It is an essential element of the Riemann zeta function, and thus is closely connected to the famous Riemann Hypothesis. I hope I do not have to explain that the derivatives of a function that has fundamental importance in analysis (calculus) have great significance themselves.

Please do not remove this and similar pages from Wikipedia. They are useful, valuable, and quite significant in the field of mathematics. Skummafremdygest (talk) 11:01, 6 June 2022 (UTC)


 * I removed the template. Joanico (talk) 11:14, 8 November 2022 (UTC)