New approximations of the gamma function in terms of the digamma function

نویسنده

  • Cristinel Mortici
چکیده

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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عنوان ژورنال:
  • Appl. Math. Lett.

دوره 23  شماره 

صفحات  -

تاریخ انتشار 2010