Talk:Dilogarithm: Difference between revisions

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) [reply ]

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) [reply ]

Changed from:

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

to:

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

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