Fungrim entry: dd5e3a

\left|\Gamma\!\left(x + y i\right)\right| \lt \left|\Gamma\!\left(x + t i\right)\right|

Assumptions:

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \,\mathbin{\operatorname{and}}\, t \in \mathbb{R} \,\mathbin{\operatorname{and}}\, \left|y\right| \gt \left|t\right|

TeX:

\left|\Gamma\!\left(x + y i\right)\right| \lt \left|\Gamma\!\left(x + t i\right)\right|

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \,\mathbin{\operatorname{and}}\, t \in \mathbb{R} \,\mathbin{\operatorname{and}}\, \left|y\right| \gt \left|t\right|

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`GammaFunction`	$\Gamma\!\left(z\right)$	Gamma function
`ConstI`	$i$	Imaginary unit
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("dd5e3a"),
    Formula(Less(Abs(GammaFunction(Add(x, Mul(y, ConstI)))), Abs(GammaFunction(Add(x, Mul(t, ConstI)))))),
    Variables(x, y, t),
    Assumptions(And(Element(x, RR), Element(y, RR), Element(t, RR), Greater(Abs(y), Abs(t)))))

Topics using this entry

Bounds and inequalities for the gamma function