LegendreFunctions#

class osaft.core.functions.LegendreFunctions[source]#

Bases: object

This class gathers all reoccurring Legendre Functions necessary for the osaft package.

Public Methods:

cos_poly(theta, coefficients)

Sum of Legendre polynomial with a cosine function as an argument

cos_monomial(degree, theta, coefficient)

Returns a single term of Legendre Cosine series

first_cos_poly(theta, coefficients)

Sum of associate Legendre Polynomial of order one with a cosine as input variable

first_cos_monomial(degree, theta, coefficient)

Returns a single term of associate Legendre Cosine series of the first order
static cos_monomial(degree, theta, coefficient)[source]#

Returns a single term of Legendre Cosine series

Parameters:

  • degree (int) – degree of the polynomial to be returned

  • theta (float) – angle

  • coefficient (complex) – coefficients of the polynomial

Return type:

float

static cos_poly(theta, coefficients)[source]#

Sum of Legendre polynomial with a cosine function as an argument

Parameters:

  • theta (float) – angle

  • coefficients (ndarray) – coefficients of the polynomial

Return type:

ndarray

static first_cos_monomial(degree, theta, coefficient)[source]#

Returns a single term of associate Legendre Cosine series of the first order

Parameters:

  • degree (int) – degree of the term

  • theta (float) – angle

  • coefficient (complex) – coefficient of the polynomial

Return type:

float

static first_cos_poly(theta, coefficients)[source]#

Sum of associate Legendre Polynomial of order one with a cosine as input variable

Parameters:

  • theta (float) – angle

  • coefficients (ndarray) – coefficients of the polynomial

Return type:

ndarray