Abstract
We prove some Lambert series identities which were stated by Gosper without proof or reference. As an application we shall evaluate integrals involving Ramanujan theta function ψ(q). Furthermore, motivated by Ramanujan identities for qψ4(q2) and ψ ψ 3 (q ( 3 q ) ), we shall evaluate the squares of qψ4(q2) and ψ ψ 3 (q ( 3 q ) ) in terms of Lambert series.
Original language | English |
---|---|
Pages (from-to) | 4451-4464 |
Number of pages | 14 |
Journal | Proceedings of the American Mathematical Society |
Volume | 147 |
Issue number | 10 |
DOIs | |
Publication status | Published - Jan 1 2019 |
Keywords
- Integrals
- Lambert series
- Q-trigonometric functions
- Ramanujan theta functions
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics