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Journals / Constructive Mathematical Analysis / 2021 / Cilt: 4 Sayı: 4

Parameterized families of polylog integrals

Anthony SOFO
Necdet BATİR
Pages
400–419
Publication Date
2021-12-13
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the process of the investigation we recover some known Euler sum equalities and discover some new identities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:It is commonly known that integrals containing log-polylog integrands admit representations in terms of special functions such as the Dirichlet eta and Dirichlet beta functions.
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Key Findings & Data:We investigate two parameterized families of such integrals and in a particular case demonstrate a connection with the Herglotz function.
💡
Conclusion & Impact:In the process of the investigation we recover some known Euler sum equalities and discover some new identities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Harmonic number · gamma function · alternating harmonic number

Abstract

It is commonly known that integrals containing log-polylog integrands admit representations in terms of special functions such as the Dirichlet eta and Dirichlet beta functions. We investigate two parameterized families of such integrals and in a particular case demonstrate a connection with the Herglotz function. In the process of the investigation we recover some known Euler sum equalities and discover some new identities.

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Cite This Article

SOFO, A., BATİR, N. (2021). Parameterized families of polylog integrals. Constructive Mathematical Analysis, Cilt: 4 Sayı: 4, 400–419. https://ajindex.com/articles/903636

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