Ramanujan's ''lost'' notebook. V: Euler's partition identity
Let \(S(m,q)=\prod_{1\leq n\leq m}(1+q^ n)\), and \(T(m,q)=\prod_{1\leq n\leq m}(1-q^{2n-1})^{-1}\). Euler noted that \(S(\infty,q)=T(\infty,q)\). In this note, the author proves two identities from Ramanujan's ''lost'' notebook, expansions of \(\sum_{m\geq 0}(S(\infty,q)-S(m,q))\), and \(\sum_{m\geq 0}(T(\infty,q)-T(m,q))\), and sets them in a more general context.
scientific article; zbMATH DE number 3968665
scientific article