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# Fungrim entry: cfefa9

$\operatorname{agm}\!\left(1, 1 + x\right) = \sum_{n=0}^{\infty} \frac{\text{A060691}\!\left(n\right)}{{8}^{n}} {\left(-x\right)}^{n}$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|x\right| < 1$
References:
• Sequence A060691 in Sloane's On-Line Encyclopedia of Integer Sequences (OEIS)
TeX:
\operatorname{agm}\!\left(1, 1 + x\right) = \sum_{n=0}^{\infty} \frac{\text{A060691}\!\left(n\right)}{{8}^{n}} {\left(-x\right)}^{n}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|x\right| < 1
Definitions:
Fungrim symbol Notation Short description
AGM$\operatorname{agm}\!\left(a, b\right)$ Arithmetic-geometric mean
Sum$\sum_{n} f(n)$ Sum
SloaneA$\text{A00000X}\!\left(n\right)$ Sequence X in Sloane's OEIS
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Abs$\left|z\right|$ Absolute value
Source code for this entry:
Entry(ID("cfefa9"),
Formula(Equal(AGM(1, Add(1, x)), Sum(Mul(Div(SloaneA("060691", n), Pow(8, n)), Pow(Neg(x), n)), For(n, 0, Infinity)))),
Variables(x),
Assumptions(And(Element(x, CC), Less(Abs(x), 1))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC