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Fungrim entry: fe4967

0θ2 ⁣(0,it)θ4 ⁣(0,it)dt=log ⁣(3+22)\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
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
ConstIii Imaginary unit
Infinity\infty Positive infinity
Loglog(z)\log(z) Natural logarithm
Sqrtz\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)))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-11-19 15:10:20.037976 UTC