Talk:Digamma function

message: 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)
thread_title: Computing Digamma

message: 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)
thread_title: Rapidly convergent series needed

message: In this equation, for one,
: u_n=\frac{p(n)}{q(n)}=\sum_{k=1}^m \frac{a_k}{n+b_k}.
,   appear throughout the section.  Is there
some way to introduce them when \frac{p(n)}{q(n)} first appears?
Is  the order
of the rational function, which is assumed in proper form, and is it
also assumed that  are the coefficients of  while
the  are those of , and that somehow it's 
guaranteed that expressions involving  are okay
to treat as if  = 0 when k > the degree of ?
I mean that's just all guesses I made working backwards, and then
looking in the Rational_function article.  (No such unexplained variables
show up there.)
Or is it just that, "Well, yeah,
p, q, a, b, and m-- it goes without saying?"
SteveWitham (talk) 06:01, 22 March 2020 (UTC)
thread_title:  Variables m, a_k and b_k in "Evaluation of sums of rational functions" 

message: 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)
thread_title:  Generalization of sum formula (multiplication theorem) 

message: 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)
thread_title:  Web Calculators 

message: The article includes two graphs of the digamma 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?  yoyo (talk) 04:57, 27 June 2015 (UTC)
replies: text: I did a search for images created by the uploarder (Image Search), and found a description of the coloring as domain coloring.   Specifically, on a similarly colored plot of Klein's J-invariant function (image), there is the link Visualizing complex-valued functions with Matplotlib and Mayavi, showing how to do this in Python. Jimw338 (talk) 16:56, 7 January 2016 (UTC)
thread_title:  Colours in graphs 

message: "The digamma function, often denoted also as  or \digamma (after the shape of the archaic Greek letter Ϝ digamma)..."
Right, but then why do we use an unadorned psi without the zero? I can understand not wanting to use a real digamma, given that it is probably not the most common usage, but this seems a bit self-contradictory without accompanying explanation. ψ is after all the general symbol for all the polygamma functions: is it just that ψ0 is the most common and is hence understood? Double sharp (talk) 09:27, 24 September 2015 (UTC)
thread_title:  Notation 

message: It would be nice to know what the Digamma function is used for.  — Preceding unsigned comment added by Chrisranderson (talk • contribs) 18:24, 12 July 2016 (UTC)
thread_title:  Application 

message: Hey. The page does not mention the poles of the digamma function at all (not that they exist, where they are, what their residues are etc.)
It is, however, mentioned on the "Polygamma function"-article. Could we mention the poles, or at least have a reference to the Polygamma-article ?  — Preceding unsigned comment added by Amusing numbers (talk • contribs) 18:25, 19 May 2022 (UTC)
thread_title:  Please mention the poles of the digamma function