I omitted a sign. The session was actually In[1]:= Sum[Log[n] x^n, {n,1,Infinity}] (1,0) Out[1]= -PolyLog [0, x] * [See P.S.] Hmm, since PolyLog[n,x] := Sum{x^k/k^n, {k,1,Infinity}], it's easy to check that ∂/∂n of this is ∂/∂n [Sum{x^k/k^n, {k,1,Infinity}] = -Sum[Log[k] x^k, {k,1,Infinity}] Help! I can only write in Mathematicese. ________________________________________________________________________________ P.S. Maybe the (1,0) superscript on PolyLog means the partial derivative with respect to the first variable. I.e., Sum[Log[n] x^n,{n,1,Infinity}] = -∂(PolyLog[n,z])/∂n (0,x). As everyone else doubtless already knew: Yes! In exactly one line on this page this notation (1,0) f[x,y] is used implicitly. Hmm, probably standard mathematical notation. Duh. On Aug 29, 2014, at 9:19 PM, Dan Asimov <dasimov@earthlink.net> wrote:

Mathematica gives

(1,0) PolyLog [0,x]

, but refuses to explain the notation.

??PolyLog ->

----- PolyLog[n, z] gives the polylogarithm function Li (z) n .PolyLog[n, p, z] gives the Nielsen generalized polylogarithm function

S (z). n, p -----

--Dan

On Aug 29, 2014, at 4:40 PM, David Wilson <davidwwilson@comcast.net> wrote:

...

Is there a closed form for

f(x) = SUM n=1..inf (ln(n)*x^n)

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