treams.special¶

Special (mathematical) functions.

Special mathematical functions used in treams. Some functions are reexported from scipy.special. Most functions are available as Numpy universal functions (numpy.ufunc) or as generalized universal functions (Generalized universal function API).

Available functions¶

Bessel and Hankel functions, with their spherical counterparts, derivatives¶

`hankel1_d`
`hankel2_d`
`jv_d`
`yv_d`
`spherical_hankel1`
`spherical_hankel2`
`spherical_hankel1_d`
`spherical_hankel2_d`

Those functions are just reexported from Scipy. So, one only needs to import this subpackage within treams.

`hankel1`(v, z[, out])	Hankel function of the first kind.
`hankel2`(v, z[, out])	Hankel function of the second kind.
`jv`(v, z[, out])	Bessel function of the first kind of real order and complex argument.
`yv`(v, z[, out])	Bessel function of the second kind of real order and complex argument.
`spherical_jn`(n, z[, derivative])	Spherical Bessel function of the first kind or its derivative.
`spherical_yn`(n, z[, derivative])	Spherical Bessel function of the second kind or its derivative.

Those functions just wrap Scipy functions with special optional arguments to be able to analogously access them like their non-spherical counterparts:

`spherical_jn_d`(n, z)	Derivative of the spherical Bessel function of the first kind.
`spherical_yn_d`(n, z)	Derivative of the spherical Bessel function of the second kind.

Scipy functions with enhanced domain¶

`sph_harm`
`lpmv`

Integrals for the Ewald summation¶

`incgamma`
`intkambe`

Wigner d- and Wigner D-matrix elements¶

`wignersmalld`
`wignerd`

Wigner 3j-symbols¶

wigner3j

Vector wave functions¶

`pi_fun`
`tau_fun`

Spherical waves and translation coefficients

`vsh_X`
`vsh_Y`
`vsh_Z`
`vsw_M`
`vsw_N`
`vsw_A`
`vsw_rM`
`vsw_rN`
`vsw_rA`
`tl_vsw_A`
`tl_vsw_B`
`tl_vsw_rA`
`tl_vsw_rB`

Cylindrical waves

`vcw_M`
`vcw_N`
`vcw_A`
`vcw_rM`
`vcw_rN`
`vcw_rA`
`tl_vcw`
`tl_vcw_r`

Plane waves

`vpw_M`
`vpw_N`
`vpw_A`

Coordinate system transformations¶

`car2cyl`
`car2sph`
`cyl2car`
`cyl2sph`
`sph2car`
`sph2cyl`
`vcar2cyl`
`vcar2sph`
`vcyl2car`
`vcyl2sph`
`vsph2car`
`vsph2cyl`
`car2pol`
`pol2car`
`vcar2pol`
`vpol2car`

Cython module¶

cython_special

Cython versions of special functions.