An approximation formula for n!

Abstract

We prove the following very accurate approximation formula for the factorial function: n!≈ n n e −n s 2π µ n + 1 6 + which is established by C. Mortici in his very new paper [8].

Asymptotic approximations for non-integer order derivatives of monomials

“…[13] Theorem 3: Let f (x) be a monomial of the form f (x) = x p , p ∈ Z + and, for very large n, let n! be approximated by n!…”

An Asymptotic Expansion for the Generalized Gamma Function

“…k − log r ≈ 0.5772156649 is Euler-Mascheroni's constant. For more details on bounds of the functions Γ(v) and d r dv r ψ(v), please refer to [3][4][5][6][7] and the references therein. Many of such bounds deduced from the monotonicity properties of some functions involving Γ or ψ.…”

Ceros de polinomios aleatorios trigonométricos

“…inferiormente, para esto se utiliza una aproximación del factorial. En [3] se menciona que, para cualquier natural, en particular k − j se satisfacen las siguientes desigualdades (12) (k…”