def METHOD_NAME():
    assert myexpand(lerchphi(1, s, a), zeta(s, a))
    assert myexpand(lerchphi(z, s, 1), polylog(s, z)/z)
    # direct summation
    assert myexpand(lerchphi(z, -1, a), a/(1 - z) + z/(1 - z)**2)
    assert myexpand(lerchphi(z, -3, a), None)
    # polylog reduction
    assert myexpand(lerchphi(z, s, Rational(1, 2)),
                    2**(s - 1)*(polylog(s, sqrt(z))/sqrt(z)
                                - polylog(s, polar_lift(-1)*sqrt(z))/sqrt(z)))
    assert myexpand(lerchphi(z, s, 2), -1/z + polylog(s, z)/z**2)
    assert myexpand(lerchphi(z, s, Rational(3, 2)), None)
    assert myexpand(lerchphi(z, s, Rational(7, 3)), None)
    assert myexpand(lerchphi(z, s, -Rational(1, 3)), None)
    assert myexpand(lerchphi(z, s, -Rational(5, 2)), None)
    # hurwitz zeta reduction
    assert myexpand(lerchphi(-1, s, a),
                    2**(-s)*zeta(s, a/2) - 2**(-s)*zeta(s, (a + 1)/2))
    assert myexpand(lerchphi(I, s, a), None)
    assert myexpand(lerchphi(-I, s, a), None)
    assert myexpand(lerchphi(exp(2*I*pi/5), s, a), None)