code: def gammatone_erb_constants(n):
    
    tnt = 2 * n - 2
    return (factorial(n - 1) ** 2 / (pi * factorial(tnt) * 2 ** -tnt),
            2 * (2 ** (1. / n) - 1) ** .5
           )
docs: Constants for using the real bandwidth in the gammatone filter, given its
    order. Returns a pair :math:`(x, y) = (1/a_n, c_n)`.
  
    Based on equations from:
  
      ``Holdsworth, J.; Patterson, R.; Nimmo-Smith, I.; Rice, P. Implementing a
      GammaTone Filter Bank. In: SVOS Final Report, Annex C, Part A: The
      Auditory Filter Bank. 1988.``
  
    First returned value is a bandwidth compensation for direct use in the
    gammatone formula:
  
    >>> x, y = gammatone_erb_constants(4)
    >>> central_frequency = 1000
    >>> round(x, 3)
    1.019
    >>> bandwidth = x * erb["moore_glasberg_83"](central_frequency)
    >>> round(bandwidth, 2)
    130.52
  
    Second returned value helps us find the ``3 dB`` bandwidth as:
  
    >>> x, y = gammatone_erb_constants(4)
    >>> central_frequency = 1000
    >>> bandwidth3dB = x * y * erb["moore_glasberg_83"](central_frequency)
    >>> round(bandwidth3dB, 2)
    113.55