Journal
JOURNAL OF INEQUALITIES AND APPLICATIONS
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1186/s13660-018-1646-6
Keywords
Gamma function; Monotonicity; Convexity; Approximation
Categories
Funding
- Fundamental Research Funds for the Central Universities [2015ZD29]
- Higher School Science Research Funds of Hebei Province of China [Z2015137]
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In this paper, we present a very accurate approximation for the gamma function: G(x+1)similar to root 2 pi x(x/e)(x()xsinh1/x)(x/2)exp(7/324 1/x(3(35)x(2)+33))=W-2 (X) as x infinity, and we prove that the function x -> In Gamma(x+ 1) - In W-2(x) is strictly decreasing and convex from (1, infinity) onto (0,beta), where beta=22,025/22,032 - In root 2 pi sinh 1 approximate to 0.00002407.
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