def test_chebyshev(): assert chebyshevt(0, x) == 1 assert chebyshevt(1, x) == x assert chebyshevt(2, x) == 2*x**2 - 1 assert chebyshevt(3, x) == 4*x**3 - 3*x assert chebyshevt(-2, x) == 2*x**2 - 1 for n in range(1, 4): for k in range(n): z = chebyshevt_root(n, k) assert chebyshevt(n, z) == 0 pytest.raises(ValueError, lambda: chebyshevt_root(n, n)) for n in range(1, 4): for k in range(n): z = chebyshevu_root(n, k) assert chebyshevu(n, z) == 0 pytest.raises(ValueError, lambda: chebyshevu_root(n, n)) n = Symbol('n') X = chebyshevt(n, x) assert isinstance(X, chebyshevt) assert chebyshevt(n, -x) == (-1)**n*chebyshevt(n, x) assert chebyshevt(-n, x) == chebyshevt(n, x) assert chebyshevt(n, oo) == oo assert chebyshevt(n, 0) == cos(pi*n/2) assert chebyshevt(n, 1) == 1 assert conjugate(chebyshevt(n, x)) == chebyshevt(n, conjugate(x)) assert diff(chebyshevt(n, x), x) == n*chebyshevu(n - 1, x) pytest.raises(ArgumentIndexError, lambda: chebyshevt(n, x).fdiff(1)) X = chebyshevu(n, x) assert isinstance(X, chebyshevu) assert chebyshevu(n, -x) == (-1)**n*chebyshevu(n, x) assert chebyshevu(-n, x) == -chebyshevu(n - 2, x) assert chebyshevu(n, oo) == oo assert chebyshevu(n, 0) == cos(pi*n/2) assert chebyshevu(n, 1) == n + 1 assert chebyshevu(-1, x) == 0 assert chebyshevu(-2, x) == -1 assert conjugate(chebyshevu(n, x)) == chebyshevu(n, conjugate(x)) assert diff(chebyshevu(n, x), x) == \ (-x*chebyshevu(n, x) + (n + 1)*chebyshevt(n + 1, x))/(x**2 - 1) pytest.raises(ArgumentIndexError, lambda: chebyshevu(n, x).fdiff(1))
def test_chebyshev(): assert chebyshevt(0, x) == 1 assert chebyshevt(1, x) == x assert chebyshevt(2, x) == 2*x**2 - 1 assert chebyshevt(3, x) == 4*x**3 - 3*x assert chebyshevt(-2, x) == 2*x**2 - 1 for n in range(1, 4): for k in range(n): z = chebyshevt_root(n, k) assert chebyshevt(n, z) == 0 pytest.raises(ValueError, lambda: chebyshevt_root(n, n)) for n in range(1, 4): for k in range(n): z = chebyshevu_root(n, k) assert chebyshevu(n, z) == 0 pytest.raises(ValueError, lambda: chebyshevu_root(n, n)) n = Symbol("n") X = chebyshevt(n, x) assert isinstance(X, chebyshevt) assert chebyshevt(n, -x) == (-1)**n*chebyshevt(n, x) assert chebyshevt(-n, x) == chebyshevt(n, x) assert chebyshevt(n, oo) == oo assert chebyshevt(n, 0) == cos(pi*n/2) assert chebyshevt(n, 1) == 1 assert conjugate(chebyshevt(n, x)) == chebyshevt(n, conjugate(x)) assert diff(chebyshevt(n, x), x) == n*chebyshevu(n - 1, x) pytest.raises(ArgumentIndexError, lambda: chebyshevt(n, x).fdiff(1)) X = chebyshevu(n, x) assert isinstance(X, chebyshevu) assert chebyshevu(n, -x) == (-1)**n*chebyshevu(n, x) assert chebyshevu(-n, x) == -chebyshevu(n - 2, x) assert chebyshevu(n, oo) == oo assert chebyshevu(n, 0) == cos(pi*n/2) assert chebyshevu(n, 1) == n + 1 assert chebyshevu(-1, x) == 0 assert chebyshevu(-2, x) == -1 assert conjugate(chebyshevu(n, x)) == chebyshevu(n, conjugate(x)) assert diff(chebyshevu(n, x), x) == \ (-x*chebyshevu(n, x) + (n + 1)*chebyshevt(n + 1, x))/(x**2 - 1) pytest.raises(ArgumentIndexError, lambda: chebyshevu(n, x).fdiff(1))