Divergent series in Gauss's diary and their extensions
Abstract
Two divergent series in Entry 7 of Gauss's diary are extended systematically by introducing additional parameters. Rogers-Fine identities, Ramanujan's continued fractions and Heine's transformation relations of basic hypergeometric series are applied to find equivalent alternative series, which enable us to compute the sums of divergent series in question.
Fields of Study & Subjects
Advanced Mathematical Identities
Mathematical functions and polynomials
History and Theory of Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 January 2026
- Document type
- Preprint