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Fungrim entry: 5033c7

\pi = 2 e \int_{0}^{\infty} \frac{\cos(x)}{{x}^{2} + 1} \, dx

TeX:

\pi = 2 e \int_{0}^{\infty} \frac{\cos(x)}{{x}^{2} + 1} \, dx

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`ConstE`	$e$	The constant e (2.718...)
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Cos`	$\cos(z)$	Cosine
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("5033c7"),
    Formula(Equal(Pi, Mul(Mul(2, ConstE), Integral(Div(Cos(x), Add(Pow(x, 2), 1)), For(x, 0, Infinity))))))

Topics using this entry

Pi

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2021-03-15 19:12:00.328586 UTC