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Fungrim entry: 4a2ac8

Γ ⁣(x+yi)Γ(x)\left|\Gamma\!\left(x + y i\right)\right| \le \left|\Gamma(x)\right|
Assumptions:xRandyRx \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R}
References:
  • B. C. Carlson (1977), Special functions of applied mathematics, Academic Press. Inequality 3.10-3.
TeX:
\left|\Gamma\!\left(x + y i\right)\right| \le \left|\Gamma(x)\right|

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
GammaFunctionΓ(z)\Gamma(z) Gamma function
ConstIii Imaginary unit
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("4a2ac8"),
    Formula(LessEqual(Abs(GammaFunction(Add(x, Mul(y, ConstI)))), Abs(GammaFunction(x)))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))),
    References("B. C. Carlson (1977), Special functions of applied mathematics, Academic Press. Inequality 3.10-3."))

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2019-10-05 13:11:19.856591 UTC