Two remarkable doubly exponential series transformations of Ramanujan
The paper deals with two transformation formulas for double exponential series, as e.g. \[ \alpha \sum_{k=0}^ \infty \exp (-ne^{k\alpha}), \] which can be found in Ramanujan's second note book. The authors remark that the formulas there are of asymptotic nature only and give exact identities which are proven using Poisson's summation formula as the main tool.
scientific article; zbMATH DE number 562817