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Journals / Constructive Mathematical Analysis / 2021 / Volume: 4 Issue: 4

Parameterized families of polylog integrals

Anthony Sofo(victoria university, melbourne, australia)0000-0002-1277-8296
Necdet Batir(NEVŞEHİR HACI BEKTAŞ VELİ ÜNİVERSİTESİ, AVANOS MESLEK YÜKSEKOKULU, MİMARLIK VE ŞEHİR PLANLAMA BÖLÜMÜ)0000-0003-0125-497X
Pages
—
Publication Date
2021-12-13
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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.
📊
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.

🔖

Cite This Article

Sofo, A., Batir, N. (2021). Parameterized families of polylog integrals. Constructive Mathematical Analysis, Volume: 4 Issue: 4. https://doi.org/10.33205/cma.1006384

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