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arXiv · 1702.05635

On special Riemann xi function formulae of Hardy involving the digamma function

Alexander E Patkowski
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Abstract

We consider some properties of integrals considered by Hardy and Koshliakov, and which have also been further extended recently by Dixit. We establish a new general integral formula from some observations about the digamma function. We also obtain lower and upper bounds for Hardy's integral through properties of the digamma function.

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Alexander E Patkowski. 2020-05-20. On special Riemann xi function formulae of Hardy involving the digamma function. https://doi.org/10.14232/actasm-020-664-3

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