orthax.orthint

orthax.orthint(c, rec, m=1, k=[], lbnd=0, scl=1, axis=0)Source 

Integrate an orthogonal series.

Returns the orthogonal series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want scl to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2 while [[1,2],[1,2]] represents 1*P_0(x)*P_0(y) + 1*P_1(x)*P_0(y) + 2*P_0(x)*P_1(y) + 2*P_1(x)*P_1(y) if axis=0 is x and axis=1 is y.

Parameters:

c (array_like) – Array of orthogonal series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.
rec (AbstractRecurrenceRelation) – Recurrence relation for the family of orthogonal polynomials
m (int, optional) – Order of integration, must be positive. (Default: 1)
k ({[], list, scalar}, optional) – Integration constant(s). The value of the first integral at lbnd is the first value in the list, the value of the second integral at lbnd is the second value, etc. If k == [] (the default), all constants are set to zero. If m == 1, a single scalar can be given instead of a list.
lbnd (scalar, optional) – The lower bound of the integral. (Default: 0)
scl (scalar, optional) – Following each integration the result is multiplied by scl before the integration constant is added. (Default: 1)
axis (int, optional) – Axis over which the integral is taken. (Default: 0).

Returns:

S (ndarray) – Orthogonal series coefficient array of the integral.

Raises:

ValueError – If m < 0, len(k) > m, np.ndim(lbnd) != 0, or np.ndim(scl) != 0.