Noam Shalev

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math.NT2026

Borwein-Bradley-type identities for Ramanujan-type series for $1/ π^{4}$

Noam Shalev

We prove ten conjectures of Z.-W. Sun on Ramanujan-type series for $1/ π^{4}$ and $π^{4}$ with harmonic numbers. They follow by comparing Taylor coefficients in new Borwein-Bradley-type…

math.NT2025

Closed-form evaluations of log-sine integrals and Apéry-like sums in terms of polylogarithms

Noam Shalev

We present a new systematic method for evaluating generalized log-sine integrals in terms of polylogarithms. Our approach is based on an identity connecting ordinary generating fun…

Borwein-Bradley-type identities for Ramanujan-type series for 1/π4

Closed-form evaluations of log-sine integrals and Apéry-like sums in terms of polylogarithms

Borwein-Bradley-type identities for Ramanujan-type series for $1/ π^{4}$