# Fungrim entry: ff5e82

$z \left({n}^{2} + 5 n + 6\right) a_{n + 3} + \left({n}^{2} + 5 n + 6\right) a_{n + 2} + z a_{n + 1} + a_{n} = 0\; \text{ where } a_{n} = \frac{{\operatorname{sinc}}^{(n)}(z)}{n !}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}$
TeX:
z \left({n}^{2} + 5 n + 6\right) a_{n + 3} + \left({n}^{2} + 5 n + 6\right) a_{n + 2} + z a_{n + 1} + a_{n} = 0\; \text{ where } a_{n} = \frac{{\operatorname{sinc}}^{(n)}(z)}{n !}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
Sinc$\operatorname{sinc}(z)$ Sinc function
Factorial$n !$ Factorial
CC$\mathbb{C}$ Complex numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("ff5e82"),
Assumptions(And(Element(z, CC), Element(n, ZZGreaterEqual(0)))))