On series identities of Gosper and integrals of Ramanujan theta function $\psi(q)$

Mohamed El Bachraoui

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arXiv · 1812.06396

On series identities of Gosper and integrals of Ramanujan theta function $\psi(q)$

Mohamed El Bachraoui

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Abstract

We prove some Lambert series which were stated by Gosper without proof or reference. As an application, we shall evaluate integrals involving Ramanujan theta function $\psi(q)$. Furthermore, motivated by Ramanujan's identities for $q\psi^4(q^2)$ and $\fr{\psi^3(q)}{\psi(q^3)}$, we shall evaluate the squares of $q\psi^4(q^2)$ and $\fr{\psi^3(q)}{\psi(q^3)}$ in terms of Lambert series.

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Mohamed El Bachraoui. 2018-12-16. On series identities of Gosper and integrals of Ramanujan theta function $\psi(q)$. https://arxiv.org/abs/1812.06396

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