# Fungrim entry: 4a1b00

$\sum_{n=-\infty}^{\infty} \operatorname{sinc}^{7}\!\left(n\right) = \frac{129423 \pi - 201684 {\pi}^{2} + 144060 {\pi}^{3} - 54880 {\pi}^{4} + 11760 {\pi}^{5} - 1344 {\pi}^{6} + 64 {\pi}^{7}}{23040}$
TeX:
\sum_{n=-\infty}^{\infty} \operatorname{sinc}^{7}\!\left(n\right) = \frac{129423 \pi - 201684 {\pi}^{2} + 144060 {\pi}^{3} - 54880 {\pi}^{4} + 11760 {\pi}^{5} - 1344 {\pi}^{6} + 64 {\pi}^{7}}{23040}
Definitions:
Fungrim symbol Notation Short description
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
Sinc$\operatorname{sinc}(z)$ Sinc function
Infinity$\infty$ Positive infinity
Pi$\pi$ The constant pi (3.14...)
Source code for this entry:
Entry(ID("4a1b00"),
Formula(Equal(Sum(Pow(Sinc(n), 7), For(n, Neg(Infinity), Infinity)), Div(Add(Sub(Add(Sub(Add(Sub(Mul(129423, Pi), Mul(201684, Pow(Pi, 2))), Mul(144060, Pow(Pi, 3))), Mul(54880, Pow(Pi, 4))), Mul(11760, Pow(Pi, 5))), Mul(1344, Pow(Pi, 6))), Mul(64, Pow(Pi, 7))), 23040))))

## 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