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Fungrim entry: 99c077

Jn ⁣(z)=1π0πcos ⁣(ntzsin(t))dtJ_{n}\!\left(z\right) = \frac{1}{\pi} \int_{0}^{\pi} \cos\!\left(n t - z \sin(t)\right) \, dt
Assumptions:nZ  and  zCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
J_{n}\!\left(z\right) = \frac{1}{\pi} \int_{0}^{\pi} \cos\!\left(n t - z \sin(t)\right) \, dt

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
Piπ\pi The constant pi (3.14...)
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Coscos(z)\cos(z) Cosine
Sinsin(z)\sin(z) Sine
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("99c077"),
    Formula(Equal(BesselJ(n, z), Mul(Div(1, Pi), Integral(Cos(Sub(Mul(n, t), Mul(z, Sin(t)))), For(t, 0, Pi))))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZ), Element(z, CC))))

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2020-04-08 16:14:44.404316 UTC