New approximations of the gamma function in terms of the digamma function
نویسندگان
چکیده
منابع مشابه
New approximations of the gamma function in terms of the digamma function
The goal of this paper is to prove the following asymptotic formula Γ (x) ≈ √ 2πe−b (x+ b) x exp ( −x− 1 2 ψ (x+ c) ) as x ∈ N, x→∞, where Γ is the Euler Gamma function and ψ is the digamma function, namely, the logarithmic derivative of Γ. Moreover, optimal values of parameters b, c are calculated in such a way that this asymptotic convergence is the best possible.
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2010
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.08.012