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Fungrim entry: 4a1b00

n=sinc7 ⁣(n)=129423π201684π2+144060π354880π4+11760π51344π6+64π723040\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
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Infinity\infty Positive infinity
Piπ\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))))

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2020-08-27 09:56:25.682319 UTC