A Note on a Method of Computing the Gamma Function

In the present paper we introduce some expansions which use the falling factorials for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Faá di Bruno formula, Bell polynomials, potential polynomials, Mittag-Leffler ...

In this paper, we establish two families of approximations for the gamma function: $$ \begin{array}{lll} {\varGamma}(x+1)&=\sqrt{2\pi x}{\left({\frac{x+a}{{\mathrm{e}}}}\right)}^x {\left({\frac{x+a}{x-a}}\right)}^{-\frac{x}{2}+\frac{1}{4}} {\left({\frac{...

In [1] Ward described the “downhill” method for determining roots of f(z) = 0, whqere f(z) is analytic. He denoted by R(x, y) and J(x, y) the real and imaginary parts, respectively, of f(z) and defined the surface W by (1) W(x, y) = | R(x, y) | + | J (x,...