Fungrim home page

Fungrim entry: 06260c

1Γ(z)eπR/2RR+1/2   where R=z\left|\frac{1}{\Gamma(z)}\right| \le {e}^{\pi R / 2} {R}^{R + 1 / 2}\; \text{ where } R = \left|z\right|
Assumptions:zCz \in \mathbb{C}
\left|\frac{1}{\Gamma(z)}\right| \le {e}^{\pi R / 2} {R}^{R + 1 / 2}\; \text{ where } R = \left|z\right|

z \in \mathbb{C}
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
GammaΓ(z)\Gamma(z) Gamma function
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(LessEqual(Abs(Div(1, Gamma(z))), Where(Mul(Exp(Div(Mul(Pi, R), 2)), Pow(R, Add(R, Div(1, 2)))), Equal(R, Abs(z))))),
    Assumptions(Element(z, CC)))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC