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Fungrim entry: f2a0c7

0θ1 ⁣(0,it)dt=2π\int_{0}^{\infty} \theta'_{1}\!\left(0 , i t\right) \, dt = 2 \pi
TeX:
\int_{0}^{\infty} \theta'_{1}\!\left(0 , i t\right) \, dt = 2 \pi
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
Piπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("f2a0c7"),
    Formula(Equal(Integral(JacobiTheta(1, 0, Mul(ConstI, t), 1), For(t, 0, Infinity)), Mul(2, Pi))))

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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