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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

Euler sums and non-integerness of harmonic type sums

Haydar Göral(DOKUZ EYLUL UNIVERSITY)0000-0002-8814-6295
Doğa Can Sertbaş(CUMHURIYET UNIVERSITY)0000-0002-5884-6856
Sayfa
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Yayın Tarihi
2020-04-02
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we analyze generalized hyperharmonic numbers in terms of topology and relate this to non-integerness.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We show that Euler sums of generalized hyperharmonic numbers can be evaluated in terms of Euler sums of generalized harmonic numbers and special values of the Riemann zeta function.
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Temel Bulgular & Veri:Then we focus on the non-integerness of generalized hyperharmonic numbers.
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Sonuç & Katkı:Finally, we analyze generalized hyperharmonic numbers in terms of topology and relate this to non-integerness.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Harmonic numbers · hyperharmonic numbers · Euler sums

Abstract

We show that Euler sums of generalized hyperharmonic numbers can be evaluated in terms of Euler sums of generalized harmonic numbers and special values of the Riemann zeta function. Then we focus on the non-integerness of generalized hyperharmonic numbers. We prove that almost all generalized hyperharmonic numbers are not integers and our error term is sharp and the best possible. Finally, we analyze generalized hyperharmonic numbers in terms of topology and relate this to non-integerness.

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Bu Makaleye Atıf Yap

Göral, H., Sertbaş, D. C. (2020). Euler sums and non-integerness of harmonic type sums. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.544489

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