Assumptions:
TeX:
\sum_{n=0}^{\infty} {2 n \choose n} {x}^{n} = \frac{1}{\sqrt{1 - 4 x}} x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|x\right| < \frac{1}{4}
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
Sum | Sum | |
Binomial | Binomial coefficient | |
Pow | Power | |
Infinity | Positive infinity | |
Sqrt | Principal square root | |
CC | Complex numbers | |
Abs | Absolute value |
Source code for this entry:
Entry(ID("2b2066"), Formula(Equal(Sum(Mul(Binomial(Mul(2, n), n), Pow(x, n)), For(n, 0, Infinity)), Div(1, Sqrt(Sub(1, Mul(4, x)))))), Variables(x), Assumptions(And(Element(x, CC), Less(Abs(x), Div(1, 4)))))