Talk:Digamma function

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[edit] Silly Question

Does anyone know why a function named after one Greek letter is usually denoted by a different greek letter? Why say but write ψ? 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)

[edit] 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)

[edit] Generalization of sum formula (multiplication theorem)

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

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)