# Fungrim entry: f5887b

$\int_{-\infty}^{\infty} \operatorname{sinc}\!\left(x + \pi n\right) \operatorname{sinc}\!\left(x + \pi m\right) \, dx = \begin{cases} \pi, & n = m\\0, & n \ne m\\ \end{cases}$
Assumptions:$n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}$
TeX:
\int_{-\infty}^{\infty} \operatorname{sinc}\!\left(x + \pi n\right) \operatorname{sinc}\!\left(x + \pi m\right) \, dx = \begin{cases} \pi, & n = m\\0, & n \ne m\\ \end{cases}

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Sinc$\operatorname{sinc}(z)$ Sinc function
Pi$\pi$ The constant pi (3.14...)
Infinity$\infty$ Positive infinity
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("f5887b"),
Formula(Equal(Integral(Mul(Sinc(Add(x, Mul(Pi, n))), Sinc(Add(x, Mul(Pi, m)))), For(x, Neg(Infinity), Infinity)), Cases(Tuple(Pi, Equal(n, m)), Tuple(0, NotEqual(n, m))))),
Variables(n, m),
Assumptions(And(Element(n, ZZ), Element(m, ZZ))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC