Fungrim home page

Fungrim entry: f89d5a

0(θ4 ⁣(0,it)1)dt=π6\int_{0}^{\infty} \left(\theta_{4}\!\left(0 , i t\right) - 1\right) \, dt = -\frac{\pi}{6}
TeX:
\int_{0}^{\infty} \left(\theta_{4}\!\left(0 , i t\right) - 1\right) \, dt = -\frac{\pi}{6}
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("f89d5a"),
    Formula(Equal(Integral(Parentheses(Sub(JacobiTheta(4, 0, Mul(ConstI, t)), 1)), For(t, 0, Infinity)), Neg(Div(Pi, 6)))))

Topics using this entry

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