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Fungrim entry: 06260c

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

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("06260c"),
    Formula(LessEqual(Abs(Div(1, GammaFunction(z))), Where(Mul(Exp(Div(Mul(ConstPi, R), 2)), Pow(R, Add(R, Div(1, 2)))), Equal(R, Abs(z))))),
    Variables(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.

2019-06-18 07:49:59.356594 UTC