A continued fraction approximation of the gamma function
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Publication:1947301
DOI10.1016/j.jmaa.2012.11.023zbMath1333.40001OpenAlexW2083868407MaRDI QIDQ1947301
Publication date: 22 April 2013
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.11.023
Gamma, beta and polygamma functions (33B15) Continued fractions; complex-analytic aspects (30B70) Approximation to limiting values (summation of series, etc.) (40A25) Convergence and divergence of continued fractions (40A15)
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Cites Work
- Unnamed Item
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- Unnamed Item
- A new Stirling series as continued fraction
- New asymptotic expansion for the gamma function
- On an asymptotic series and corresponding continued fraction for a gamma function ratio
- Continued fractions and the polygamma functions
- Asymptotic series and Stieltjes continued fractions for a gamma function ratio
- Stieltjes continued fractions for polygamma functions; speed of convergence
- Ramanujan's continued fraction for products of gamma functions
- Product Approximations via Asymptotic Integration
- OPTIMIZING THE RATE OF CONVERGENCE IN SOME NEW CLASSES OF SEQUENCES CONVERGENT TO EULER'S CONSTANT
- On Stieltjes' Continued Fraction for the Gamma Function
- Decision procedure for indefinite hypergeometric summation
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