Alladi-GrinsteadConstant

*To*: mathgroup at smc.vnet.net*Subject*: [mg113189] Alladi-GrinsteadConstant*From*: Peter Pein <petsie at dordos.net>*Date*: Sun, 17 Oct 2010 06:06:46 -0400 (EDT)

Dear Group, please have a look at the following: It is OK for me to return an unevaluated sum: In[1]:= Sum[-(Log[1 - 1/k]/k), {k, 2, Infinity}] Out[1]= Sum[-(Log[1 - 1/k]/k), {k, 2, Infinity}] it has got a value: In[2]:= NSum[-(Log[1 - 1/k]/k), {k, 2, Infinity}] Out[2]= 0.7885305658471413 to try it as double sum, get the seriescoeffs: SeriesCoefficient[-(Log[1 - 1/k]/k), {k, Infinity, n}] Out[3]= Piecewise[{{1/(-1 + n), n >= 2}}, 0] and feed this into Mathematica: Sum[1/(k^n*(n - 1)), {n, 2, Infinity}, {k, 2, Infinity}] Out[4]= -Infinity MINUS Infinity???? The same with a big N: NSum[1/(k^n*(n - 1)), {n, 2, Infinity}, {k, 2, Infinity}] Out[5]= 0.7885305658584437 In[6]:= Exp[% - 1] Out[6]= 0.8093940204976885 In[7]:= $Version Out[7]= 7.0 for Linux x86 (64-bit) (February 18, 2009) Will this be fixed in Version 8?