orthax.laguerre.lagmulx

orthax.laguerre.lagmulx(c, mode='full')Source

Multiply a Laguerre series by x.

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

Parameters:

• c (array_like) – 1-D array of Laguerre 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

lagadd, lagsub, lagmul, lagdiv, lagpow

Notes

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

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

Examples

>>> from orthax.laguerre import lagmulx
>>> lagmulx([1, 2, 3])
array([-1.,  -1.,  11.,  -9.])