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Fungrim entry: d39c46

J1/3 ⁣(z)=12ω(3Ai ⁣(ω2)3Bi ⁣(ω2))   where ω=(3z2)1/3J_{1 / 3}\!\left(z\right) = \frac{1}{2 \omega} \left(3 \operatorname{Ai}\!\left(-{\omega}^{2}\right) - \sqrt{3} \operatorname{Bi}\!\left(-{\omega}^{2}\right)\right)\; \text{ where } \omega = {\left(\frac{3 z}{2}\right)}^{1 / 3}
Assumptions:zC{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
J_{1 / 3}\!\left(z\right) = \frac{1}{2 \omega} \left(3 \operatorname{Ai}\!\left(-{\omega}^{2}\right) - \sqrt{3} \operatorname{Bi}\!\left(-{\omega}^{2}\right)\right)\; \text{ where } \omega = {\left(\frac{3 z}{2}\right)}^{1 / 3}

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
AiryAiAi ⁣(z)\operatorname{Ai}\!\left(z\right) Airy function of the first kind
Powab{a}^{b} Power
Sqrtz\sqrt{z} Principal square root
AiryBiBi ⁣(z)\operatorname{Bi}\!\left(z\right) Airy function of the second kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("d39c46"),
    Formula(Equal(BesselJ(Div(1, 3), z), Where(Mul(Div(1, Mul(2, omega)), Sub(Mul(3, AiryAi(Neg(Pow(omega, 2)))), Mul(Sqrt(3), AiryBi(Neg(Pow(omega, 2)))))), Equal(omega, Pow(Div(Mul(3, z), 2), Div(1, 3)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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2019-09-20 18:07:53.062439 UTC