Binet's second formula, Hermite's generalization, and two related identities
Abstract: Legendre was the first to evaluate two well-known integrals involving sines and exponentials. One of these integrals can be used to prove Binet’s second formula for the logarithm of the gamma function. Here, we show that the other integral leads to a specific case of Hermite’s generalization of Binet’s formula. From the analogs of Legendre’s integrals, with sines replaced by cosines, we obtain two integration identities involving logarithms and trigonometric functions. Using these identities, we then subsequently derive generalizations of Binet’s and Hermite’s formulas involving the integral of a complex logarithm.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Binet's second formula, Hermite's generalization, and two related identities ; volume:21 ; number:1 ; year:2023 ; extent:15
Open mathematics ; 21, Heft 1 (2023) (gesamt 15)
- Creator
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Boyack, Rufus
- DOI
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10.1515/math-2022-0568
- URN
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urn:nbn:de:101:1-2023040314030519242418
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 10:53 AM CEST
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Associated
- Boyack, Rufus
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