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 functionz (
complex
) – argument of the functioni (
int
, optional) – i-th derivative is computedDefault: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 functionz (
complex
) – argument of the functioni (
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 functionz (
complex
) – argument of the functioni (
int
, optional) – i-th derivative is computedDefault: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 functionz (
complex
) – argument of the functioni (
int
, optional) – i-th derivative is computedDefault:0
- Return type:
complex
- static besselj(n, z)[source]#
Spherical Bessel function of the first kind of order n
- Parameters:
n (
int
) – Orderz (
complex
) – argument
- Return type:
complex
- static bessely(n, z)[source]#
Spherical Bessel function of the second kind of order n
- Parameters:
n (
int
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
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
) – orderz (
complex
) – argument
- Return type:
complex