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Fungrim entry: d60119

agm ⁣(ca,cb)=cagm ⁣(a,b)\operatorname{agm}\!\left(c a, c b\right) = c \operatorname{agm}\!\left(a, b\right)
Assumptions:aC  and  bC  and  cC  and  (a=0  or  b=0  or  c=0  or  ba(,0])a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(a = 0 \;\mathbin{\operatorname{or}}\; b = 0 \;\mathbin{\operatorname{or}}\; c = 0 \;\mathbin{\operatorname{or}}\; \frac{b}{a} \notin \left(-\infty, 0\right]\right)
\operatorname{agm}\!\left(c a, c b\right) = c \operatorname{agm}\!\left(a, b\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(a = 0 \;\mathbin{\operatorname{or}}\; b = 0 \;\mathbin{\operatorname{or}}\; c = 0 \;\mathbin{\operatorname{or}}\; \frac{b}{a} \notin \left(-\infty, 0\right]\right)
Fungrim symbol Notation Short description
AGMagm ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(AGM(Mul(c, a), Mul(c, b)), Mul(c, AGM(a, b)))),
    Variables(a, b, c),
    Assumptions(And(Element(a, CC), Element(b, CC), Element(c, CC), Or(Equal(a, 0), Equal(b, 0), Equal(c, 0), NotElement(Div(b, a), OpenClosedInterval(Neg(Infinity), 0))))))

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2021-03-15 19:12:00.328586 UTC