New asymptotic formulas and inequalities for the gamma function based on continued fractions

DOI10.1007/S00025-018-0785-XzbMath1390.33006OpenAlexW2790044913MaRDI QIDQ1743252

Xiaoguang Wang, Lixin Song, Junying Wang, Dawei Lu

Publication date: 13 April 2018

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-018-0785-x

zbMATH Keywords

gamma functioninequalitiesrate of convergencecontinued fraction

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Continued fractions (11A55) Rate of convergence, degree of approximation (41A25)

Cites Work

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• Efficient approximations of the gamma function and further properties
• A new Stirling series as continued fraction
• New asymptotic expansion for the gamma function
• An ultimate extremely accurate formula for approximation of the factorial function
• A continued fraction approximation of the gamma function
• A new quicker sequence convergent to Euler's constant
• Product Approximations via Asymptotic Integration
• Decision procedure for indefinite hypergeometric summation
• Ramanujan's Lost Notebook

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