NJAS>Bill, your integrand eta[q^4]^8/eta[q^2]^4 has expansion x+4*x^3+6*x^5+8*x^7+13*x^9+12*x^11+14*x^13+24*x^15+18*x^17+20*x^19+... whose coefficients are A008438, "sum of divisors of 2n+1" A008438 has a lot of Ramanujan-type formulas. Neil Right, it's merely A008438/{2,4,6,8,...}. Minor. There's also a variant with eight triangular numbers. (I.e., the integrand^2). Another reference, suggested by Timothy Ngo: http://www.math.wisc.edu/~ono/reprints/006.pdf --rwg On Sat, Jun 1, 2013 at 7:24 AM, Bill Gosper <billgosper@gmail.com> wrote: but it is a little startling. [Correcting etq -> eta] With eta[q] := q^(1/24) (q;q)₀₀, In[532]:=Integrate[eta[q^4]^8/eta[q^2]^4, q]/q In[533]:= Series[%,{q,0,105}] Out[533]= q/2+q^3+q^5+q^7+(13 q^9)/10+q^11+q^13+(3 q^15)/2+q^17+q^19+(16 q^21)/11+q^23+(31 q^25)/26+(10 q^27)/7+q^29+q^31+(24 q^33)/17+(4 q^35)/3+q^37+(7 q^39)/5+q^41+q^43+(39 q^45)/23+q^47+(57 q^49)/50+(18 q^51)/13+q^53+(9 q^55)/7+(40 q^57)/29+q^59+q^61+(13 q^63)/8+(14 q^65)/11+q^67+(48 q^69)/35+q^71+q^73+(31 q^75)/19+(16 q^77)/13+q^79+(121 q^81)/82+q^83+(54 q^85)/43+(15 q^87)/11+q^89+(28 q^91)/23+(64 q^93)/47+(5 q^95)/4+q^97+(39 q^99)/25+q^101+q^103+(96 q^105)/53+O[q]^(1261/12) I.e., the coeff of q^n is 1 iff n is an odd prime. --rwg No, Fred, that word is "bulbitated". On 5/29/13, Adam P. Goucher <apgoucher@gmx.com> wrote: Yes, and Dave Greene has archives dating from April 1992, when math-fun bifurcated. Fred>Hope it didn't ruin the carpet ...