def sphere_analytical_gaussian(dr, a, alpha=0.2765):
    """
    Analytically calculate the sphere's functional form by convolving the
    Heavyside function with first order approximation to the sinc, a Gaussian.
    The alpha parameters controls the width of the approximation -- should be
    1, but is fit to be roughly 0.2765
    """
    term1 = 0.5*(erf((dr+2*a)/(alpha*np.sqrt(2))) + erf(-dr/(alpha*np.sqrt(2))))
    term2 = np.sqrt(0.5/np.pi)*(alpha/(dr+a+1e-10)) * (
                np.exp(-0.5*dr**2/alpha**2) - np.exp(-0.5*(dr+2*a)**2/alpha**2)
            )
    return term1 - term2
def sphere_analytical_gaussian(dr, a, alpha=0.2765):
    """
    Analytically calculate the sphere's functional form by convolving the
    Heavyside function with first order approximation to the sinc, a Gaussian.
    The alpha parameters controls the width of the approximation -- should be
    1, but is fit to be roughly 0.2765
    """
    term1 = 0.5*(erf((dr+2*a)/(alpha*np.sqrt(2))) + erf(-dr/(alpha*np.sqrt(2))))
    term2 = np.sqrt(0.5/np.pi)*(alpha/(dr+a+1e-10)) * (
                np.exp(-0.5*dr**2/alpha**2) - np.exp(-0.5*(dr+2*a)**2/alpha**2)
            )
    return term1 - term2
def sphere_analytical_gaussian ( dr , a , alpha = 0.2765 ) : term1 = 0.5 * ( erf ( ( dr + 2 * a ) / ( alpha * np . sqrt ( 2 ) ) ) + erf ( - dr / ( alpha * np . sqrt ( 2 ) ) ) ) term2 = np . sqrt ( 0.5 / np . pi ) * ( alpha / ( dr + a + 1e-10 ) ) * ( np . exp ( - 0.5 * dr ** 2 / alpha ** 2 ) - np . exp ( - 0.5 * ( dr + 2 * a ) ** 2 / alpha ** 2 ) ) return term1 - term2
Analytically calculate the sphere's functional form by convolving the
    Heavyside function with first order approximation to the sinc, a Gaussian.
    The alpha parameters controls the width of the approximation -- should be
    1, but is fit to be roughly 0.2765
Analytically calculate the sphere s functional form by convolving the Heavyside function with first order approximation to the sinc a Gaussian . The alpha parameters controls the width of the approximation -- should be 1 but is fit to be roughly 0 . 2765