Fungrim entry: fe4967

\int_{0}^{\infty} \theta_{2}\!\left(0 , i t\right) \theta_{4}\!\left(0 , i t\right) \, dt = \log\!\left(3 + 2 \sqrt{2}\right)

TeX:

\int_{0}^{\infty} \theta_{2}\!\left(0 , i t\right) \theta_{4}\!\left(0 , i t\right) \, dt = \log\!\left(3 + 2 \sqrt{2}\right)

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
`Log`	$\log(z)$	Natural logarithm
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("fe4967"),
    Formula(Equal(Integral(Mul(JacobiTheta(2, 0, Mul(ConstI, t)), JacobiTheta(4, 0, Mul(ConstI, t))), For(t, 0, Infinity)), Log(Add(3, Mul(2, Sqrt(2)))))))

Topics using this entry

Integrals of Jacobi theta functions

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