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Bessel function of first kind

`J = besselj(`

computes the Bessel function of the first kind
`nu`

,`Z`

)*J*_{ν}(*z*) for each element in array `Z`

.

The Bessel functions are related to the Hankel functions, also called Bessel functions of the third kind:

$$\begin{array}{l}{H}_{\nu}^{(1)}(z)={J}_{\nu}(z)+i\text{\hspace{0.17em}}{Y}_{\nu}(z)\\ {H}_{\nu}^{(2)}(z)={J}_{\nu}(z)-i\text{\hspace{0.17em}}{Y}_{\nu}(z).\end{array}$$

$${H}_{\nu}^{(K)}(z)$$ is `besselh`

, *J*_{ν}(*z*) is `besselj`

, and *Y*_{ν}(*z*) is `bessely`

. The Hankel functions also form a
fundamental set of solutions to Bessel's equation (see `besselh`

).