On the Circular Summation of the Eleventh Powers of Ramanujanʹs Theta Function Original Research Article

Letf(a, b) denote Ramanujanʹs theta series. In his “Lost Notebook”, Ramanujan claimed that the “circular” summation ofnth powers offsatisfies a factorization of the formf(an, bn) Fn(anbn) whereFn(q)=1+2nq(n−1)/2+…. Moreover, he listed explicit closed formulas forF2,F3,F4,F5, andF7. Berndt and Son have asked for a similar expression for any otherFn. Here we obtain such an expression forF11(q).