# `special._spherical_bessel`¶

## Module Contents¶

### Functions¶

 `spherical_jn`(n,z,derivative=False) rSpherical Bessel function of the first kind or its derivative. `spherical_yn`(n,z,derivative=False) rSpherical Bessel function of the second kind or its derivative. `spherical_in`(n,z,derivative=False) rModified spherical Bessel function of the first kind or its derivative. `spherical_kn`(n,z,derivative=False) rModified spherical Bessel function of the second kind or its derivative.
`spherical_jn`(n, z, derivative=False)

rSpherical Bessel function of the first kind or its derivative.

Defined as [1]_,

where is the Bessel function of the first kind.

n : int, array_like
Order of the Bessel function (n >= 0).
z : complex or float, array_like
Argument of the Bessel function.
derivative : bool, optional
If True, the value of the derivative (rather than the function itself) is returned.

jn : ndarray

For real arguments greater than the order, the function is computed using the ascending recurrence [2]_. For small real or complex arguments, the definitional relation to the cylindrical Bessel function of the first kind is used.

The derivative is computed using the relations [3]_,

New in version 0.18.0.

`spherical_yn`(n, z, derivative=False)

rSpherical Bessel function of the second kind or its derivative.

Defined as [1]_,

where is the Bessel function of the second kind.

n : int, array_like
Order of the Bessel function (n >= 0).
z : complex or float, array_like
Argument of the Bessel function.
derivative : bool, optional
If True, the value of the derivative (rather than the function itself) is returned.

yn : ndarray

For real arguments, the function is computed using the ascending recurrence [2]_. For complex arguments, the definitional relation to the cylindrical Bessel function of the second kind is used.

The derivative is computed using the relations [3]_,

New in version 0.18.0.

`spherical_in`(n, z, derivative=False)

rModified spherical Bessel function of the first kind or its derivative.

Defined as [1]_,

where is the modified Bessel function of the first kind.

n : int, array_like
Order of the Bessel function (n >= 0).
z : complex or float, array_like
Argument of the Bessel function.
derivative : bool, optional
If True, the value of the derivative (rather than the function itself) is returned.

in : ndarray

The function is computed using its definitional relation to the modified cylindrical Bessel function of the first kind.

The derivative is computed using the relations [2]_,

New in version 0.18.0.

`spherical_kn`(n, z, derivative=False)

rModified spherical Bessel function of the second kind or its derivative.

Defined as [1]_,

where is the modified Bessel function of the second kind.

n : int, array_like
Order of the Bessel function (n >= 0).
z : complex or float, array_like
Argument of the Bessel function.
derivative : bool, optional
If True, the value of the derivative (rather than the function itself) is returned.

kn : ndarray

The function is computed using its definitional relation to the modified cylindrical Bessel function of the second kind.

The derivative is computed using the relations [2]_,

New in version 0.18.0.