Fixed in 11.3

NSum[Log[k]/k^k, {k,1,Infinity}, WorkingPrecision->50]
(* 0.219947267975228664843531307905860703797097130 *)


Sum[Log[k]/k^k, {k,1,Infinity}]
(* -(PolyLog^(1,0))[0,1/k] *)

What does "k" in the result? Bug ?

  • 1
    $\begingroup$ It's really Times[-1,Derivative[1,0][PolyLog][0,Power[k,-1]]]. I get the same result on on Mac. I'd call it a bug. $\endgroup$
    – John Doty
    Dec 10, 2017 at 13:53
  • 1
    $\begingroup$ Problem continues thru v11.2 on Mac $\endgroup$
    – Bob Hanlon
    Dec 10, 2017 at 14:26
  • 1
    $\begingroup$ This is quite obviously a bug. NSum[Log[k]/k^k, {k, 1, Infinity}] evaluates to 0.219947, and it obviously shouldn't have a $k$ in the output. I'm adding the tag. (V10.0.1 on Mac OSX). $\endgroup$
    – march
    Dec 11, 2017 at 4:24
  • $\begingroup$ BTW, Wolfram Alpha gives the same troublesome result. $\endgroup$ Dec 11, 2017 at 6:53
  • $\begingroup$ Versions 5.2.0 and 8.0.4 give the same wrong result, moreover, the result from 5.2.0 contains the variable "K$18" instead of "k". $\endgroup$
    – innaiz
    Dec 11, 2017 at 7:26

1 Answer 1



In 11.3 the result is returned as unevaluated. So the issue was bypassed. Much better to return unevaluated, than return something not correct.

Mathematica graphics

Compare to version 11.2

Mathematica graphics


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