Talk:Dilogarithm

Full article?

Is the intent here to write a full article? All it does currently is refer to dilogarithm, which refers back to polylogarithm. Why should polylogarithm link here, then? - Gauge 00:06, 11 August 2005 (UTC)

the relationship is two-fold: 1. if someone's looking for Spence's function, he might be looking for either definition, but only one is a polylogarithm, hence the difference has to be made clear 2. if someone reading up on polylogarithms wants to know about spence's function he'll go here, and see the two different definitions. Hence I think the current state is satisfying.

OTOH if anybody wants to expand the article with the history of Spence's integral or whatever, he can of course do so, I think it is more appropriate to add this information to the article on Polylogarithms. 217.237.151.171 20:06, 26 September 2005 (UTC)

Errorfix June 10, 2009

Changed from:

$F(z)=\int _{0}^{z}{\ln(1+\zeta ) \over \zeta }$

to:

$F(z)=-\int _{0}^{z}{\ln(1+\zeta ) \over \zeta }$

I do not know where the original definition was taken from, but it was inconsistent with the series expansion. One of the two had to switch sign. To confirm, you can check e.g. with Mathematica:

In[1]:= Series[-Integrate[Log[1 + x]/x, {x, 0, a}], {a, 0, 3}]
              2    3
             a    a        4
Out[1]= -a + -- - -- + O[a]
             4    9  

AmitAronovitch (talk • contribs) 14:23, 10 June 2009 (UTC)

Errorfix Aug 23 2012

I am writing C code to compute the dialog on the complex plane. I have found errors in several online sources concerning special values. I made one fix for Li2(–(1+√5)/2) with three sources of corroboration. I am confident in the change that I have made but I think that there is another error in Li2(–(√5-1)/2) as well. These expressions are devilishly error prone to manipulate and I am surprised that there are not more errors. I may do more editing when I have checked my results in a few independent ways. — Preceding unsigned comment added by NormHardy (talk • contribs) 05:02, 24 August 2012 (UTC)

My edits after 2012 Aug 23 were not wrong, but are complex and misleading. I wish I could get back to the Aug 23 state whereupon I could fix everything by merely changing two signs. I attempted to undo my edits but I evidently do not understand the logic of "undo". My attempts seem not to have taken effect. My fixes deleted some correct 'source' text that was in the wrong place. NormHardy (talk) 00:00, 25 August 2012 (UTC)

I think that the errors that I spotted are all fixed now. I could not undo the previous botched fixes. In case you doubt the substance of the fix note that the dilogarithm function is monotonic increasing from –∞ to 1. Sorry for the messy history. NormHardy (talk) 03:20, 28 August 2012 (UTC)

There are two special values given for real arguments greater than 1. Such arguments are on the conventional cut for the dilog. Function values are complex there. I get: Li2(2) = 2.4674011002723399 ± 2.1775860903036022i Li2((3+√5)/2) = 2.4003296863799677 ± 3.0235430688555738i to which I see no relation to those now given. 99.4.121.168 (talk) 14:31, 30 August 2012 (UTC)

Intro

The +/- shortcut in the introduction kills the whole article. Clarity is more important than brevity Wlod (talk) 20:10, 23 May 2013 (UTC)

Why this is called Spence's function ? All the references talk about the dilogarithm ! — Preceding unsigned comment added by 147.250.1.2 (talk) 16:14, 19 May 2015 (UTC)

Too technical?

To me, the Too Technical template message seems inappropriate to this topic. Anyone object if I remove it?

Tesspub (talk) 17:29, 19 June 2020 (UTC)

Should this be moved to dilogarithm?

The name "dilogarithm" is 2+ orders of magnitude more common than "Spence's function" in the academic literature. –jacobolus (t) 21:15, 30 November 2023 (UTC)

I agree. I performed the move, as it seems unlikely to be controversial. Adumbrativus (talk) 05:18, 14 December 2023 (UTC)

Identities crisis?

In the section Identities, the very first identity appears to me as if the factor of 1/2 either belongs to the other side of the equation, or equivalently is left where it is but changed to a 2.

I hope someone knowledgeable about the dilogarithm function will fix this.

Nobody knows what "reflection" means

In the introductory section it is mentioned that two functions are referred to as "Spence's" function: the dilogarithm "and its reflection".

But nobody knows what kind of reflection this means.

It is much better to say exactly what you mean here, instead of obscuring information with ambiguous words like "reflection".

Likewise, this passage requires much better writing

Also in the introductory section, one passage is as follows:

"In hyperbolic geometry the dilogarithm can be used to compute the volume of an ideal simplex. Specifically, a simplex whose vertices have cross ratio z has hyperbolic volume ...."

But absolutely no background has been stated, so this sentence comes across as utter nonsense to anyone who doesn't already know about it.

Like, What dimension are we talking about??? (I know the answer because the cross-ratio was used; most readers will not.)

Like: Which model of hyperbolic geometry are we talking about here???

Without much clearer writing, your words will not succeed in carrying any information to most readers, the ones who most need it.