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Fungrim entry: ecb406

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

TeX:

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

Definitions:

Fungrim symbol	Notation	Short description
`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
`Pi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("ecb406"),
    Formula(Equal(Integral(JacobiTheta(2, 0, Mul(ConstI, t)), For(t, 0, Infinity)), Pi)))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC