# Talk:Digamma function

WikiProject Mathematics (Rated Start-class, Low-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Low Importance
Field: Analysis

## Computing Digamma

It looks like link to Cephes is incorrect (I was not able to find digamma there). On the other hand GNU Scientific Library and Boost Math Library provide implementations of digamma for C and C++ respectively. Perhaps somebody with better knowledge could create section on numerical approximations of digamma (see also remark by linas)? Rzolau (talk) 23:51, 4 April 2009 (UTC)

## Silly Question

Does anyone know why a function named after one Greek letter is usually denoted by a different greek letter? Why say $\digamma$ but write $\psi$? 130.94.162.64 08:43, 25 November 2005 (UTC)

Huh? Ohh. Seems that wiki-TeX is rendering \digamma as a captial F instead of \psi with a prime on it. Strange. I will ask at Wikipedia talk:WikiProject Mathematics. linas 16:22, 25 November 2005 (UTC)
Oh, right. Yes, I have seen this as an alternate notation for the digamma. Its rare, I think, but not so rare that TeX didn't decide to create a special symbol for it. As you know, in math, there just aren't enough symbols. linas 17:01, 25 November 2005 (UTC)
Note that the name of the archaic Greek letter digamma, (="double gamma"), that was the Greek version of "F", is due to the its shape $\digamma,$ that is formed by two capital letters "Γ", one over the other. I would be very curious to know who introduced the name digamma for the logarithmic derivative of the Gamma function. Certainly he alluded to the shape of the fraction $\frac{\Gamma'}{\Gamma},$ and it is too bad that this philological joke has been a bit spoiled by the choice of the letter Ψ, that has nothing to do with $\digamma$, not to speak about the dumb neologism "polygamma". I think the TeX \digamma renders a true digamma, as it has to be, primarily because D.Knuth is a fine scholar. --pma (talk) 15:55, 6 December 2009 (UTC)

## Rapidly convergent series needed

I need a a series expression for the digamma that is rapidly convergent, so that it can be used for high-precision numeric calculations. This article lacks such a beast...

Maybe the Borwein Tchebeysheff-polynomial trick for the rapid calculation of the Riemann zeta can be extended to the Hurwitz zeta. Then the digamma can be obtained from there ... anyone have a reference for this? linas 20:12, 22 April 2006 (UTC)

## Generalization of sum formula (multiplication theorem)

A small generalization of the sum formula (or multiplication theorem) is:

$\sum_{p=0}^{q-1}\psi(a+p/q)=q\psi(qa)-q\ln(q)$

and may be seen to be consistent with the original (current) formula by setting:

$a=1/q$,

for q a natural number.

Hair Commodore 19:58, 28 October 2006 (UTC)

## Web Calculators

Last night, Arthur Rubin removed a link to an web calculator providing useful free services to users of exponential integrals. Many wikipedia articles on topics that have calculational aspects provide links to web calculators. This was the only calculator link on the article, so the link to that useful service is now gone. Web calcualtors for such relative obscrure functions are rare. Please cite an official policy justiifcation, explain your actions in light of these points, or engage in a conversation as to why you believe this information to be inappropriate. Otherwise I plan to revert the change. Ichbin-dcw (talk) 19:48, 25 May 2010 (UTC)