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Fungrim entry: 799742

0(θ3 ⁣(0,it)1)dt=π3\int_{0}^{\infty} \left(\theta_{3}\!\left(0 , i t\right) - 1\right) \, dt = \frac{\pi}{3}
\int_{0}^{\infty} \left(\theta_{3}\!\left(0 , i t\right) - 1\right) \, dt = \frac{\pi}{3}
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:
    Formula(Equal(Integral(Parentheses(Sub(JacobiTheta(3, 0, Mul(ConstI, t)), 1)), For(t, 0, Infinity)), Div(Pi, 3))))

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2021-03-15 19:12:00.328586 UTC