Estimating gamma function by 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: Mathematical and Computer Modelling
سال: 2010
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2010.05.030