BesselFunctions

class osaft.core.functions.BesselFunctions[source]

Bases: object

This class gathers all reoccurring spherical hankel and bessel functions necessary for the osaft package.

Public Methods:

`besselj`(n, z)	Spherical Bessel function of the first kind of order n
`d1_besselj`(n, z)	First derivative of the spherical Bessel function of the first kind of order n
`d2_besselj`(n, z)	Second derivative of the spherical Bessel function of the first kind of order n
`d3_besselj`(n, z)	Third derivative of the spherical Bessel function of the first kind of order n
`d4_besselj`(n, z)	Fourth derivative of the spherical Bessel function of the first kind of order n
`bessely`(n, z)	Spherical Bessel function of the second kind of order n
`d1_bessely`(n, z)	First derivative of the spherical Bessel function of the second kind of order n
`d2_bessely`(n, z)	Second derivative of the spherical Bessel function of the second kind of order n
`d3_bessely`(n, z)	Third derivative of the spherical Bessel function of the second kind of order n
`d4_bessely`(n, z)	Fourth derivative of the spherical Bessel function of the second kind of order n
`hankelh1`(n, z)	Spherical Hankel function of the first kind of order n
`d1_hankelh1`(n, z)	First derivative of the spherical Hankel function of the first kind of order n
`d2_hankelh1`(n, z)	Second derivative of the spherical Hankel function of the first kind of order n
`d3_hankelh1`(n, z)	Third derivative of the spherical Hankel function of the first kind of order n
`d4_hankelh1`(n, z)	Fourth derivative of the spherical Hankel function of the first kind of order n
`d5_hankelh1`(n, z)	Fifth derivative of the spherical Hankel function of the first kind of order n
`hankelh2`(n, z)	Spherical Hankel function of the second kind of order n
`d1_hankelh2`(n, z)	First derivative of the spherical Hankel function of the second kind of order n second kind
`d2_hankelh2`(n, z)	Second derivative of the spherical Hankel function of the second kind of order n second kind
`d3_hankelh2`(n, z)	Third derivative of the spherical Hankel function of the second kind of order n second kind
`d4_hankelh2`(n, z)	Fourth derivative of the spherical Hankel function of the second kind of order n second kind
`d5_hankelh2`(n, z)	Fifth derivative of the spherical Hankel function of the second kind of order n second kind
`adaptive_derivative_besselj`(n, z[, i])	Returns the value of the i-th derivative of the spherical Bessel function of the first kind of order n.
`adaptive_derivative_bessely`(n, z[, i])	Returns the value of the i-th derivative of the spherical Bessel function of the second kind of order n.
`adaptive_derivative_hankelh1`(n, z[, i])	Returns the value of the i-th derivative of the spherical Hankel function of order n.
`adaptive_derivative_hankelh2`(n, z[, i])	Returns the value of the i-th derivative of the spherical Hankel function of order n.

classmethod adaptive_derivative_besselj(n, z, i=0)[source]

Returns the value of the i-th derivative of the spherical Bessel function of the first kind of order n. The coefficients for the derivative are calculated at runtime.

Parameters

n (int) – order of spherical Bessel function
z (complex) – argument of the function
i (int, optional) – i-th derivative is computed
Default: 0

Return type

complex

classmethod adaptive_derivative_bessely(n, z, i=0)[source]

Returns the value of the i-th derivative of the spherical Bessel function of the second kind of order n. The coefficients for the derivative are calculated at runtime.

Parameters

n (int) – order of spherical Hankel function
z (complex) – argument of the function
i (int, optional) – i-th derivative is computed at runtime.
Default: 0

Return type

complex

classmethod adaptive_derivative_hankelh1(n, z, i=0)[source]

Returns the value of the i-th derivative of the spherical Hankel function of order n. The coefficients for the derivative are calculated at runtime.

Parameters

n (int) – order of spherical Hankel function
z (complex) – argument of the function
i (int, optional) – i-th derivative is computed
Default: 0

Return type

complex

classmethod adaptive_derivative_hankelh2(n, z, i=0)[source]

Returns the value of the i-th derivative of the spherical Hankel function of order n. The coefficients for the derivative are calculated at runtime.

Parameters

n (int) – order of spherical Hankel function
z (complex) – argument of the function
i (int, optional) – i-th derivative is computed
Default: 0

Return type

complex

static besselj(n, z)[source]

Spherical Bessel function of the first kind of order n

Parameters

n (int) – Order
z (complex) – argument

Return type

complex

static bessely(n, z)[source]

Spherical Bessel function of the second kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d1_besselj(n, z)[source]

First derivative of the spherical Bessel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d1_bessely(n, z)[source]

First derivative of the spherical Bessel function of the second kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d1_hankelh1(n, z)[source]

First derivative of the spherical Hankel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d1_hankelh2(n, z)[source]

First derivative of the spherical Hankel function of the second kind of order n second kind

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d2_besselj(n, z)[source]

Second derivative of the spherical Bessel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d2_bessely(n, z)[source]

Second derivative of the spherical Bessel function of the second kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d2_hankelh1(n, z)[source]

Second derivative of the spherical Hankel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d2_hankelh2(n, z)[source]

Second derivative of the spherical Hankel function of the second kind of order n second kind

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d3_besselj(n, z)[source]

Third derivative of the spherical Bessel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d3_bessely(n, z)[source]

Third derivative of the spherical Bessel function of the second kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d3_hankelh1(n, z)[source]

Third derivative of the spherical Hankel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d3_hankelh2(n, z)[source]

Third derivative of the spherical Hankel function of the second kind of order n second kind

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d4_besselj(n, z)[source]

Fourth derivative of the spherical Bessel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d4_bessely(n, z)[source]

Fourth derivative of the spherical Bessel function of the second kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d4_hankelh1(n, z)[source]

Fourth derivative of the spherical Hankel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d4_hankelh2(n, z)[source]

Fourth derivative of the spherical Hankel function of the second kind of order n second kind

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d5_hankelh1(n, z)[source]

Fifth derivative of the spherical Hankel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

classmethod d5_hankelh2(n, z)[source]

Fifth derivative of the spherical Hankel function of the second kind of order n second kind

Parameters

n (int) – order
z (complex) – argument

Return type

complex

static hankelh1(n, z)[source]

Spherical Hankel function of the first kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex

static hankelh2(n, z)[source]

Spherical Hankel function of the second kind of order n

Parameters

n (int) – order
z (complex) – argument

Return type

complex