# Fungrim entry: e233b0

${z}^{2} \left({r}^{2} + 7 r + 12\right) \frac{I^{(r + 4)}_{\nu}\!\left(z\right)}{\left(r + 4\right)!} + z \left(2 {r}^{2} + 11 r + 15\right) \frac{I^{(r + 3)}_{\nu}\!\left(z\right)}{\left(r + 3\right)!} + \left(r \left(r + 4\right) - {z}^{2} - {\nu}^{2} + 4\right) \frac{I^{(r + 2)}_{\nu}\!\left(z\right)}{\left(r + 2\right)!} - 2 z \frac{I^{(r + 1)}_{\nu}\!\left(z\right)}{\left(r + 1\right)!} - \frac{I^{(r)}_{\nu}\!\left(z\right)}{r !} = 0$
Assumptions:$\nu \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}$
Alternative assumptions:$\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}$
TeX:
{z}^{2} \left({r}^{2} + 7 r + 12\right) \frac{I^{(r + 4)}_{\nu}\!\left(z\right)}{\left(r + 4\right)!} + z \left(2 {r}^{2} + 11 r + 15\right) \frac{I^{(r + 3)}_{\nu}\!\left(z\right)}{\left(r + 3\right)!} + \left(r \left(r + 4\right) - {z}^{2} - {\nu}^{2} + 4\right) \frac{I^{(r + 2)}_{\nu}\!\left(z\right)}{\left(r + 2\right)!} - 2 z \frac{I^{(r + 1)}_{\nu}\!\left(z\right)}{\left(r + 1\right)!} - \frac{I^{(r)}_{\nu}\!\left(z\right)}{r !} = 0

\nu \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}

\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
BesselI$I_{\nu}\!\left(z\right)$ Modified Bessel function of the first kind
Factorial$n !$ Factorial
ZZ$\mathbb{Z}$ Integers
CC$\mathbb{C}$ Complex numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("e233b0"),
Assumptions(And(Element(nu, ZZ), Element(z, CC), Element(r, ZZGreaterEqual(0))), And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))), Element(r, ZZGreaterEqual(0)))))