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# numpy.polynomial.hermite.hermmulx

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```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(more...)
```

```        def hermmulx(c):
"""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.

Returns
-------
out : ndarray
Array representing the result of the multiplication.

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

.. math::

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

Examples
--------
>>> from numpy.polynomial.hermite import hermmulx
>>> hermmulx([1, 2, 3])
array([ 2. ,  6.5,  1. ,  1.5])

"""
# c is a trimmed copy
[c] = pu.as_series([c])
# The zero series needs special treatment
if len(c) == 1 and c[0] == 0:
return c

prd = np.empty(len(c) + 1, dtype=c.dtype)
prd[0] = c[0]*0
prd[1] = c[0]/2
for i in range(1, len(c)):
prd[i + 1] = c[i]/2
prd[i - 1] += c[i]*i
return prd
```

```    def test_hermmulx(self):
assert_equal(herm.hermmulx([0]), [0])
assert_equal(herm.hermmulx([1]), [0,.5])
for i in range(1, 5):
ser = [0]*i + [1]
tgt = [0]*(i - 1) + [i, 0, .5]
assert_equal(herm.hermmulx(ser), tgt)
```

```    def test_hermmulx(self):
assert_equal(herm.hermmulx([0]), [0])
assert_equal(herm.hermmulx([1]), [0, .5])
for i in range(1, 5):
ser = [0]*i + [1]
tgt = [0]*(i - 1) + [i, 0, .5]
assert_equal(herm.hermmulx(ser), tgt)
```