BesselFunctionOfTheFirstKind

Bessel function of the first kind (English)

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The Bessel function of the first kind of order n is written J_n(z), and defined as

J_n(z) =

⌠
⌡

π

0

cos(nt − zsin(t))dt

where n is not zero.
If n is a positive integer, this is equal to:

J_n(z) =

∞
∑
r=0

(−1)^r

r! Γ(n+r+1)







n+2r

These functions arise in the solution of the wave equation in cylindrical coordinates. They satisfy Bessel's equation.

weiterer Begriff:: (en) Function
bezieht sich auf:: (en) Bessel; (en) Bessel's equation
ist bezogen auf:: (en) Bessel function of the second kind; (en) Bessel function of the third kind; (en) Hankel transform