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arXiv · 2502.02419

On a function of Ramanujan twisted by a logarithm

Atul Dixit·Sumukha Sathyanarayana·N. Guru Sharan
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Abstract

A two-term functional equation for an infinite series involving the digamma function and a logarithmic factor is derived. A modular relation on page 220 of Ramanujan's Lost Notebook as well as a corresponding recent result for the derivative of Deninger's function are two main ingredients in its derivation. An interesting integral $\mathscr{H}(x)$, which is of independent interest, plays a prominent role in our functional equation. Several alternative representations for $\mathscr{H}(x)$ are obtained.

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Atul Dixit, Sumukha Sathyanarayana, N. Guru Sharan. 2025-02-04. On a function of Ramanujan twisted by a logarithm. https://arxiv.org/abs/2502.02419

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