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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:x∈R  and⁡  y∈Rx \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
Abs∣z∣\left|z\right| Absolute value
GammaΓ(z)\Gamma(z) Gamma function
ConstIii Imaginary unit
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("4a2ac8"),
    Formula(LessEqual(Abs(Gamma(Add(x, Mul(y, ConstI)))), Abs(Gamma(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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2021-03-15 19:12:00.328586 UTC