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.

[1]http://dlmf.nist.gov/10.47.E3
[2]http://dlmf.nist.gov/10.51.E1
[3]http://dlmf.nist.gov/10.51.E2
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.

[1]http://dlmf.nist.gov/10.47.E4
[2]http://dlmf.nist.gov/10.51.E1
[3]http://dlmf.nist.gov/10.51.E2
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.

[1]http://dlmf.nist.gov/10.47.E7
[2]http://dlmf.nist.gov/10.51.E5
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.

[1]http://dlmf.nist.gov/10.47.E9
[2]http://dlmf.nist.gov/10.51.E5