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arXiv · 2208.13876

On the Barnes double gamma function

Shahen Alexanian·Alexey Kuznetsov
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Abstract

We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function $G(z;\tau)$. Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic expansion as $z\to \infty$. Third, we derive some new properties, including a new product identity and new representations of the gamma modular forms $C(\tau)$ and $D(\tau)$.

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BibTeXRIS

Shahen Alexanian, Alexey Kuznetsov. 2022-08-29. On the Barnes double gamma function. https://doi.org/10.1080/10652469.2023.2238115

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