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Fungrim entry: a0955b

M/2N/2θ4 ⁣(x,τ)dx=NM2\int_{M / 2}^{N / 2} \theta_{4}\!\left(x , \tau\right) \, dx = \frac{N - M}{2}
Assumptions:τHandMZandNZ\tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, M \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, N \in \mathbb{Z}
TeX:
\int_{M / 2}^{N / 2} \theta_{4}\!\left(x , \tau\right) \, dx = \frac{N - M}{2}

\tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, M \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, N \in \mathbb{Z}
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
HHH\mathbb{H} Upper complex half-plane
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("a0955b"),
    Formula(Equal(Integral(JacobiTheta(4, x, tau), For(x, Div(M, 2), Div(N, 2))), Div(Sub(N, M), 2))),
    Variables(tau, M, N),
    Assumptions(And(Element(tau, HH), Element(M, ZZ), Element(N, ZZ))))

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2019-11-19 15:10:20.037976 UTC