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 ) \psi (q) . Furthermore, motivated by Ramanujan identities for q ψ 4 ( q 2 ) q\psi ^4(q^2) and ψ 3 ( q ) ψ ( q 3 ) \frac {\psi ^3(q)}{\psi (q^3)} , we shall evaluate the squares of q ψ 4 ( q 2 ) q\psi ^4(q^2) and ψ 3 ( q ) ψ ( q 3 ) \frac {\psi ^3(q)}{\psi (q^3)} in terms of Lambert series.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have