שמור ב:
| מחבר ראשי: | |
|---|---|
| פורמט: | Recurso digital |
| שפה: | |
| יצא לאור: |
Zenodo
2025
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| נושאים: | |
| גישה מקוונת: | https://doi.org/10.5281/zenodo.14916208 |
| תגים: |
הוספת תג
אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!
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תוכן הענינים:
- <p>Recently, Mneimneh published an interesting binomial sum involving harmonic numbers, generalizing an identity previously highlighted by Paule and Schneider. The new identity was derived using probabilistic analysis. Campbell proposed afterwards two different proofs, based respectively on the Zeilberger algorithm and on beta-tye integrals. In the present work, we obtain, using the Mneimneh identity combined with the Pascal inversion formula, two expressions of the harmonic numbers. The first one, which is a sum rule, involves the Lerch transcendent, and the second one, which is an explicit form, involves the Gauss hypergeometric series.</p>