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

Sinc function