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Fungrim entry: d8cb3e

\pi = \int_{0}^{\infty} \theta_{2}\!\left(0 , i t\right) \, dt

TeX:

\pi = \int_{0}^{\infty} \theta_{2}\!\left(0 , i t\right) \, dt

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`ConstI`	$i$	Imaginary unit
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("d8cb3e"),
    Formula(Equal(Pi, Integral(JacobiTheta(2, 0, Mul(ConstI, t)), For(t, 0, Infinity)))))

Topics using this entry

Pi

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