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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def expand(self, flm, nmax=None):
 """ Return the Slepian expansion coefficients of the input function. Usage ----- s = x.expand(flm, [nmax]) Returns ------- s : SlepianCoeff class instance The Slepian expansion coefficients of the input function. Parameters flm : SHCoeffs class instance The input function to expand in Slepian functions. nmax : int, optional, default = (x.lmax+1)**2 The number of Slepian expansion coefficients to compute. Description The global function f is input using its spherical harmonic expansion coefficients flm. The expansion coefficients of the function f using Slepian functions g is given by f_alpha = sum_{lm}^{lmax} f_lm g(alpha)_lm """

        if nmax is None:
            nmax = (self.lmax+1)**2
        elif nmax is not None and nmax > (self.lmax+1)**2:
            raise ValueError(
                "nmax must be less than or equal to (lmax+1)**2 " +
                "where lmax is {:s}. Input value is {:s}"
                .format(repr(self.lmax), repr(nmax))
                )

        coeffsin = flm.to_array(normalization='4pi', csphase=1, lmax=self.lmax)

        return self._expand(coeffsin, nmax)