Fungrim entry: 3fe2b0

\int_{-\infty}^{\infty} \operatorname{sinc}\!\left(x + a\right) \operatorname{sinc}\!\left(x + b\right) \, dx = \pi \operatorname{sinc}\!\left(a - b\right)

Assumptions:

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}

TeX:

\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}

Definitions:

Fungrim symbol	Notation	Short description
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Infinity`	$\infty$	Positive infinity
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("3fe2b0"),
    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))))

Topics using this entry

Sinc function