orthax.orthder

orthax.orthder(c, rec, m=1, scl=1, axis=0)Source 

Differentiate an orthogonal series.

Returns the orthogonal series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series 1*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) – Number of derivatives taken, must be non-negative. (Default: 1)
scl (scalar, optional) – Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1)
axis (int, optional) – Axis over which the derivative is taken. (Default: 0).

Returns:

der (ndarray) – Orthogonal series of the derivative.