Jν(z)=(2z)ν0F1(ν+1,−4z2)
Assumptions:ν∈Z≥0andz∈C
Alternative assumptions:ν∈Candz∈C∖{0}
TeX:
J_{\nu}\!\left(z\right) = {\left(\frac{z}{2}\right)}^{\nu} \,{}_0{\textbf F}_1\!\left(\nu + 1, -\frac{{z}^{2}}{4}\right) \nu \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \nu \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
BesselJ | Jν(z) | Bessel function of the first kind |
Pow | ab | Power |
Hypergeometric0F1Regularized | 0F1(a,z) | Regularized confluent hypergeometric limit function |
ZZGreaterEqual | Z≥n | Integers greater than or equal to n |
CC | C | Complex numbers |
Source code for this entry:
Entry(ID("ecd36f"), Formula(Equal(BesselJ(nu, z), Mul(Pow(Div(z, 2), nu), Hypergeometric0F1Regularized(Add(nu, 1), Neg(Div(Pow(z, 2), 4)))))), Variables(nu, z), Assumptions(And(Element(nu, ZZGreaterEqual(0)), Element(z, CC)), And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))))))