orthax.hermite_e.hermemulx

orthax.hermite_e.hermemulx(c, mode='full')Source

Multiply a Hermite series by x.

Multiply the Hermite series c by x, where x is the independent variable.

Parameters:

• c (array_like) – 1-D array of Hermite series coefficients ordered from low to high.

• mode ({"full", "same"}) – If “full”, output has shape (len(c) + 1). If “same”, output has shape (len(c)), possibly truncating high order modes.

Returns:

out (ndarray) – Array representing the result of the multiplication.

Notes

The multiplication uses the recursion relationship for Hermite polynomials in the form

\[xP_i(x) = (P_{i + 1}(x) + iP_{i - 1}(x)))\]

Examples

>>> from orthax.hermite_e import hermemulx
>>> hermemulx([1, 2, 3])
array([2.,  7.,  2.,  3.])