On series identities of Gosper and integrals of Ramanujan theta function 𝜓(𝑞)

El Bachraoui, Mohamed

doi:10.1090/proc/14690

On series identities of Gosper and integrals of Ramanujan theta function $\psi (q)$
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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 $\psi (q)$. Furthermore, motivated by Ramanujan identities for $q\psi ^4(q^2)$ and $\frac {\psi ^3(q)}{\psi (q^3)}$, we shall evaluate the squares of $q\psi ^4(q^2)$ and $\frac {\psi ^3(q)}{\psi (q^3)}$ in terms of Lambert series.

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