23 Jun
2019
23 Jun
'19
2:13 a.m.
Out[10]= {-(Log[7]/(2 ProductLog[-1, -(((5/(1 + E^3 Sqrt[\[Pi]]))^(1/4) Log[7])/( 2 \[Pi]))])), (8 Sqrt[3/23] \[Pi] Sinh[(Sqrt[23] \[Pi])/6])/(-1 + 2 Cosh[(Sqrt[23] \[Pi])/3])} In[11]:= N@% Out[11]= {0.368412535931434, 0.368412535931434} In[12]:= Equal @@ %% Out[12]= False The 2nd expression is, amazingly, Integrate[QPochhammer[q,q],{q,0,1}]. https://en.wikipedia.org/wiki/Euler_function I can't quite coax it out of ries. Does anyone have a closed form for Integrate[DedekindEta[Log[q]/2/I/π],{q,0,1}] ~ .3416968346182687559823? It will probably involve Gamma, which is not yet in ries. —rwg