orthax.hermite.hermmulx

orthax.hermite.hermmulx(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.

See also

hermadd, hermsub, hermmul, hermdiv, hermpow

Notes

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

\[xP_i(x) = (P_{i + 1}(x)/2 + i*P_{i - 1}(x))\]

Examples

>>> from orthax.hermite import hermmulx
>>> hermmulx([1, 2, 3])
array([2. , 6.5, 1. , 1.5])