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Fungrim entry: 3fe2b0

sinc ⁣(x+a)sinc ⁣(x+b)dx=πsinc ⁣(ab)\int_{-\infty}^{\infty} \operatorname{sinc}\!\left(x + a\right) \operatorname{sinc}\!\left(x + b\right) \, dx = \pi \operatorname{sinc}\!\left(a - b\right)
Assumptions:aC  and  bCa \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
\int_{-\infty}^{\infty} \operatorname{sinc}\!\left(x + a\right) \operatorname{sinc}\!\left(x + b\right) \, dx = \pi \operatorname{sinc}\!\left(a - b\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
Fungrim symbol Notation Short description
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Infinity\infty Positive infinity
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Integral(Mul(Sinc(Add(x, a)), Sinc(Add(x, b))), For(x, Neg(Infinity), Infinity)), Mul(Pi, Sinc(Sub(a, b))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC))))

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2021-03-15 19:12:00.328586 UTC