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Fungrim entry: 727715

∫0∞θ2 ⁣(0,it)θ3 ⁣(0,it)θ4 ⁣(0,it) dt=2\int_{0}^{\infty} \theta_{2}\!\left(0 , i t\right) \theta_{3}\!\left(0 , i t\right) \theta_{4}\!\left(0 , i t\right) \, dt = 2
TeX:
\int_{0}^{\infty} \theta_{2}\!\left(0 , i t\right) \theta_{3}\!\left(0 , i t\right) \theta_{4}\!\left(0 , i t\right) \, dt = 2
Definitions:
Fungrim symbol Notation Short description
Integral∫abf(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
Source code for this entry:
Entry(ID("727715"),
    Formula(Equal(Integral(Mul(Mul(JacobiTheta(2, 0, Mul(ConstI, t)), JacobiTheta(3, 0, Mul(ConstI, t))), JacobiTheta(4, 0, Mul(ConstI, t))), For(t, 0, Infinity)), 2)))

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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