Python dirichlet_eta Examples

Example #1

File: test_zeta_functions.py Project: goretkin/diofant

def test_rewriting():
    assert dirichlet_eta(x).rewrite(zeta) == (1 - 2**(1 - x))*zeta(x)
    assert zeta(x).rewrite(dirichlet_eta) == dirichlet_eta(x)/(1 - 2**(1 - x))
    assert tn(dirichlet_eta(x), dirichlet_eta(x).rewrite(zeta), x)
    assert tn(zeta(x), zeta(x).rewrite(dirichlet_eta), x)

    assert zeta(x, a).rewrite(lerchphi) == lerchphi(1, x, a)
    assert polylog(s, z).rewrite(lerchphi) == lerchphi(z, s, 1)*z

    assert lerchphi(1, x, a).rewrite(zeta) == zeta(x, a)
    assert z*lerchphi(z, s, 1).rewrite(polylog) == polylog(s, z)

Example #2

File: test_zeta_functions.py Project: skirpichev/diofant

def test_rewriting():
    assert dirichlet_eta(x).rewrite(zeta) == (1 - 2**(1 - x))*zeta(x)
    assert zeta(x).rewrite(dirichlet_eta) == dirichlet_eta(x)/(1 - 2**(1 - x))
    assert zeta(z, 2).rewrite(dirichlet_eta) == zeta(z, 2)
    assert zeta(z, 2).rewrite('tractable') == zeta(z, 2)
    assert tn(dirichlet_eta(x), dirichlet_eta(x).rewrite(zeta), x)
    assert tn(zeta(x), zeta(x).rewrite(dirichlet_eta), x)

    assert zeta(x, a).rewrite(lerchphi) == lerchphi(1, x, a)
    assert polylog(s, z).rewrite(lerchphi) == lerchphi(z, s, 1)*z

    assert lerchphi(1, x, a).rewrite(zeta) == zeta(x, a)
    assert z*lerchphi(z, s, 1).rewrite(polylog) == polylog(s, z)

    assert lerchphi(z, s, a).rewrite(zeta) == lerchphi(z, s, a)

Example #3

def test_polylog_eval():
    assert polylog(s, 0) == 0
    assert polylog(s, 1) == zeta(s)
    assert polylog(s, -1) == -dirichlet_eta(s)
    assert polylog(s, exp_polar(I * pi)) == polylog(s, -1)
    assert polylog(s, 2 * exp_polar(2 * I * pi)) == polylog(
        s, 2 * exp_polar(2 * I * pi), evaluate=False)

Example #4

def test_dirichlet_eta_eval():
    assert dirichlet_eta(0) == Rational(1, 2)
    assert dirichlet_eta(-1) == Rational(1, 4)
    assert dirichlet_eta(1) == log(2)
    assert dirichlet_eta(2) == pi**2 / 12
    assert dirichlet_eta(4) == pi**4 * Rational(7, 720)

Example #5

File: test_zeta_functions.py Project: skirpichev/diofant

def test_dirichlet_eta_eval():
    assert dirichlet_eta(0) == Rational(1, 2)
    assert dirichlet_eta(-1) == Rational(1, 4)
    assert dirichlet_eta(1) == log(2)
    assert dirichlet_eta(2) == pi**2/12
    assert dirichlet_eta(4) == pi**4*Rational(7, 720)

Example #6

File: test_zeta_functions.py Project: skirpichev/diofant

def test_polylog_eval():
    assert polylog(s, 0) == 0
    assert polylog(s, 1) == zeta(s)
    assert polylog(s, -1) == -dirichlet_eta(s)
    assert polylog(s, exp_polar(I*pi)) == polylog(s, -1)
    assert polylog(s, 2*exp_polar(2*I*pi)) == polylog(s, 2*exp_polar(2*I*pi), evaluate=False)