- Title
- Euler’s constant, q-logarithms, and formulas of Ramanujan and Gosper
- Creator
- Sondow, Jonathan; Zudilin, W.
- Relation
- The Ramanujan Journal Vol. 12, Issue 2, p. 225-244
- Publisher Link
- http://dx.doi.org/10.1007/s11139-006-0075-1
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2006
- Description
- The aim of the paper is to relate computational and arithmetic questions about Euler’s constant γ with properties of the values of the q-logarithm function, with natural choice of~q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca’s and Gosper’s series for γ, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler’s constant. The main tools are Euler-type integrals and hypergeometric series.
- Subject
- Euler’s constant; q-logarithm; hypergeometric series; Euler’s transform; irrationality
- Identifier
- http://hdl.handle.net/1959.13/928070
- Identifier
- uon:10331
- Identifier
- ISSN:1382-4090
- Rights
- The final publication is available at www.springerlink.com
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE2 | Author final version | 210 KB | Adobe Acrobat PDF | View Details Download |