code: def hermemulx(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) + iP_{i - 1}(x)))
  
      Examples
      --------
      >>> from numpy.polynomial.hermite_e import hermemulx
      >>> hermemulx([1, 2, 3])
      array([2.,  7.,  2.,  3.])
  
      """
      # 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]
      for i in range(1, len(c)):
          prd[i + 1] = c[i]
          prd[i - 1] += c[i] * i
      return prd
  
imports: import numpy
  import numpy.linalg
  from numpy.core.multiarray import normalize_axis_index
  from .None import polyutils
  from ._polybase import ABCPolyBase
label_desc: Use image node_id 7 for calling a global function with example usage: hermemulx(c) and returns: prd, c