def betapdfdenom(alpha, beta): return sp_funcs_m.beta(alpha, beta)
def betapdf(x, alpha, beta): return x**alpha * (1.0 - x)**beta / sp_funcs_m.beta(alpha, beta)
def betapdf(x, alpha, beta): return x**alpha * (1.0-x)**beta / sp_funcs_m.beta(alpha, beta)