Python sympy.rf函数代码示例

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本文整理汇总了Python中sympy.rf函数的典型用法代码示例。如果您正苦于以下问题：Python rf函数的具体用法？Python rf怎么用？Python rf使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。

在下文中一共展示了rf函数的17个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。

示例1: test_special_products

def test_special_products():
    # Wallis product
    assert product((4*k)**2 / (4*k**2 - 1), (k, 1, n)) == \
        4**n*factorial(n)**2/rf(Rational(1, 2), n)/rf(Rational(3, 2), n)

    # Euler's product formula for sin
    assert product(1 + a/k**2, (k, 1, n)) == \
        rf(1 - sqrt(-a), n)*rf(1 + sqrt(-a), n)/factorial(n)**2

开发者ID:A-turing-machine，项目名称:sympy，代码行数:8，代码来源:test_products.py

示例2: test_rf_ff_eval_hiprec

def test_rf_ff_eval_hiprec():
    maple = Float('6.9109401292234329956525265438452')
    us = ff(18, S(2)/3).evalf(32)
    assert abs(us - maple)/us < 1e-31

    maple = Float('6.8261540131125511557924466355367')
    us = rf(18, S(2)/3).evalf(32)
    assert abs(us - maple)/us < 1e-31

    maple = Float('34.007346127440197150854651814225')
    us = rf(Float('4.4', 32), Float('2.2', 32));
    assert abs(us - maple)/us < 1e-31

开发者ID:asmeurer，项目名称:sympy，代码行数:12，代码来源:test_comb_factorials.py

示例3: test_rf_lambdify_mpmath

def test_rf_lambdify_mpmath():
    from sympy import lambdify
    x, y = symbols('x,y')
    f = lambdify((x,y), rf(x, y), 'mpmath')
    maple = Float('34.007346127440197')
    us = f(4.4, 2.2)
    assert abs(us - maple)/us < 1e-15

开发者ID:asmeurer，项目名称:sympy，代码行数:7，代码来源:test_comb_factorials.py

示例4: test_issue_9699

def test_issue_9699():
    n, k = symbols('n k', real=True)
    x, y = symbols('x, y')
    assert combsimp((n + 1)*factorial(n)) == factorial(n + 1)
    assert combsimp((x + 1)*factorial(x)/gamma(y)) == gamma(x + 2)/gamma(y)
    assert combsimp(factorial(n)/n) == factorial(n - 1)
    assert combsimp(rf(x + n, k)*binomial(n, k)) == binomial(n, k)*gamma(k + n + x)/gamma(n + x)

开发者ID:A-turing-machine，项目名称:sympy，代码行数:7，代码来源:test_combsimp.py

示例5: test_simple_products

def test_simple_products():
    assert product(2, (k, a, n)) == 2**(n - a + 1)
    assert product(k, (k, 1, n)) == factorial(n)
    assert product(k**3, (k, 1, n)) == factorial(n)**3

    assert product(k + 1, (k, 0, n - 1)) == factorial(n)
    assert product(k + 1, (k, a, n - 1)) == rf(1 + a, n - a)

    assert product(cos(k), (k, 0, 5)) == cos(1)*cos(2)*cos(3)*cos(4)*cos(5)
    assert product(cos(k), (k, 3, 5)) == cos(3)*cos(4)*cos(5)
    assert product(cos(k), (k, 1, Rational(5, 2))) != cos(1)*cos(2)

    assert isinstance(product(k**k, (k, 1, n)), Product)

    assert Product(x**k, (k, 1, n)).variables == [k]

    raises(ValueError, lambda: Product(n))
    raises(ValueError, lambda: Product(n, k))
    raises(ValueError, lambda: Product(n, k, 1))
    raises(ValueError, lambda: Product(n, k, 1, 10))
    raises(ValueError, lambda: Product(n, (k, 1)))

    assert product(1, (n, 1, oo)) == 1  # issue 8301
    assert product(2, (n, 1, oo)) == oo
    assert product(-1, (n, 1, oo)).func is Product

开发者ID:A-turing-machine，项目名称:sympy，代码行数:25，代码来源:test_products.py

示例6: test_ff_eval_apply

def test_ff_eval_apply():
    x, y = symbols('x,y')
    n, k = symbols('n k', integer=True)
    m = Symbol('m', integer=True, nonnegative=True)

    assert ff(nan, y) == nan
    assert ff(x, nan) == nan

    assert ff(x, y) == ff(x, y)

    assert ff(oo, 0) == 1
    assert ff(-oo, 0) == 1

    assert ff(oo, 6) == oo
    assert ff(-oo, 7) == -oo

    assert ff(oo, -6) == oo
    assert ff(-oo, -7) == oo

    assert ff(x, 0) == 1
    assert ff(x, 1) == x
    assert ff(x, 2) == x*(x - 1)
    assert ff(x, 3) == x*(x - 1)*(x - 2)
    assert ff(x, 5) == x*(x - 1)*(x - 2)*(x - 3)*(x - 4)

    assert ff(x, -1) == 1/(x + 1)
    assert ff(x, -2) == 1/((x + 1)*(x + 2))
    assert ff(x, -3) == 1/((x + 1)*(x + 2)*(x + 3))

    assert ff(100, 100) == factorial(100)

    assert ff(2*x**2 - 5*x, 2) == (2*x**2  - 5*x)*(2*x**2 - 5*x - 1)
    assert isinstance(ff(2*x**2 - 5*x, 2), Mul)
    assert ff(x**2 + 3*x, -2) == 1/((x**2 + 3*x + 1)*(x**2 + 3*x + 2))

    assert ff(Poly(2*x**2 - 5*x, x), 2) == Poly(4*x**4 - 28*x**3 + 59*x**2 - 35*x, x)
    assert isinstance(ff(Poly(2*x**2 - 5*x, x), 2), Poly)
    raises(ValueError, lambda: ff(Poly(2*x**2 - 5*x, x, y), 2))
    assert ff(Poly(x**2 + 3*x, x), -2) == 1/(x**4 + 12*x**3 + 49*x**2 + 78*x + 40)
    raises(ValueError, lambda: ff(Poly(x**2 + 3*x, x, y), -2))


    assert ff(x, m).is_integer is None
    assert ff(n, k).is_integer is None
    assert ff(n, m).is_integer is True
    assert ff(n, k + pi).is_integer is False
    assert ff(n, m + pi).is_integer is False
    assert ff(pi, m).is_integer is False

    assert isinstance(ff(x, x), ff)
    assert ff(n, n) == factorial(n)

    assert ff(x, k).rewrite(rf) == rf(x - k + 1, k)
    assert ff(x, k).rewrite(gamma) == (-1)**k*gamma(k - x) / gamma(-x)
    assert ff(n, k).rewrite(factorial) == factorial(n) / factorial(n - k)
    assert ff(x, k).rewrite(binomial) == factorial(k) * binomial(x, k)

开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:56，代码来源:test_comb_factorials.py

示例7: test_simple_products

def test_simple_products():
    assert product(2, (k, a, n)) == 2**(n-a+1)
    assert product(k, (k, 1, n)) == factorial(n)
    assert product(k**3, (k, 1, n)) == factorial(n)**3

    assert product(k+1, (k, 0, n-1)) == factorial(n)
    assert product(k+1, (k, a, n-1)) == rf(1+a, n-a)

    assert product(cos(k), (k, 0, 5)) == cos(1)*cos(2)*cos(3)*cos(4)*cos(5)
    assert product(cos(k), (k, 3, 5)) == cos(3)*cos(4)*cos(5)
    assert product(cos(k), (k, 1, Rational(5, 2))) == cos(1)*cos(2)

    assert isinstance(product(k**k, (k, 1, n)), Product)

开发者ID:Grahack，项目名称:geophar，代码行数:13，代码来源:test_products.py

示例8: test_rsolve_hyper

def test_rsolve_hyper():
    assert rsolve_hyper([-1, -1, 1], 0, n) in [
        C0*(S.Half - S.Half*sqrt(5))**n + C1*(S.Half + S.Half*sqrt(5))**n,
        C1*(S.Half - S.Half*sqrt(5))**n + C0*(S.Half + S.Half*sqrt(5))**n,
    ]

    assert rsolve_hyper([n**2 - 2, -2*n - 1, 1], 0, n) in [
        C0*rf(sqrt(2), n) + C1*rf(-sqrt(2), n),
        C1*rf(sqrt(2), n) + C0*rf(-sqrt(2), n),
    ]

    assert rsolve_hyper([n**2 - k, -2*n - 1, 1], 0, n) in [
        C0*rf(sqrt(k), n) + C1*rf(-sqrt(k), n),
        C1*rf(sqrt(k), n) + C0*rf(-sqrt(k), n),
    ]

    assert rsolve_hyper(
        [2*n*(n + 1), -n**2 - 3*n + 2, n - 1], 0, n) == C1*factorial(n) + C0*2**n

    assert rsolve_hyper(
        [n + 2, -(2*n + 3)*(17*n**2 + 51*n + 39), n + 1], 0, n) == None

    assert rsolve_hyper([-n - 1, -1, 1], 0, n) == None

    assert rsolve_hyper([-1, 1], n, n).expand() == C0 + n**2/2 - n/2

    assert rsolve_hyper([-1, 1], 1 + n, n).expand() == C0 + n**2/2 + n/2

    assert rsolve_hyper([-1, 1], 3*(n + n**2), n).expand() == C0 + n**3 - n

    assert rsolve_hyper([-a, 1],0,n).expand() == C0*a**n

    assert rsolve_hyper([-a, 0, 1], 0, n).expand() == (-1)**n*C1*a**(n/2) + C0*a**(n/2)

    assert rsolve_hyper([1, 1, 1], 0, n).expand() == \
        C0*(-S(1)/2 - sqrt(3)*I/2)**n + C1*(-S(1)/2 + sqrt(3)*I/2)**n

    assert rsolve_hyper([1, -2*n/a - 2/a, 1], 0, n) == None

开发者ID:Acebulf，项目名称:sympy，代码行数:38，代码来源:test_recurr.py

示例9: test_rf_eval_apply

def test_rf_eval_apply():
    x, y = symbols('x,y')
    n, k = symbols('n k', integer=True)
    m = Symbol('m', integer=True, nonnegative=True)

    assert rf(nan, y) == nan
    assert rf(x, nan) == nan

    assert rf(x, y) == rf(x, y)

    assert rf(oo, 0) == 1
    assert rf(-oo, 0) == 1

    assert rf(oo, 6) == oo
    assert rf(-oo, 7) == -oo

    assert rf(oo, -6) == oo
    assert rf(-oo, -7) == oo

    assert rf(x, 0) == 1
    assert rf(x, 1) == x
    assert rf(x, 2) == x*(x + 1)
    assert rf(x, 3) == x*(x + 1)*(x + 2)
    assert rf(x, 5) == x*(x + 1)*(x + 2)*(x + 3)*(x + 4)

    assert rf(x, -1) == 1/(x - 1)
    assert rf(x, -2) == 1/((x - 1)*(x - 2))
    assert rf(x, -3) == 1/((x - 1)*(x - 2)*(x - 3))

    assert rf(1, 100) == factorial(100)

    assert rf(x**2 + 3*x, 2) == (x**2 + 3*x)*(x**2 + 3*x + 1)
    assert isinstance(rf(x**2 + 3*x, 2), Mul)
    assert rf(x**3 + x, -2) == 1/((x**3 + x - 1)*(x**3 + x - 2))

    assert rf(Poly(x**2 + 3*x, x), 2) == Poly(x**4 + 8*x**3 + 19*x**2 + 12*x, x)
    assert isinstance(rf(Poly(x**2 + 3*x, x), 2), Poly)
    raises(ValueError, lambda: rf(Poly(x**2 + 3*x, x, y), 2))
    assert rf(Poly(x**3 + x, x), -2) == 1/(x**6 - 9*x**5 + 35*x**4 - 75*x**3 + 94*x**2 - 66*x + 20)
    raises(ValueError, lambda: rf(Poly(x**3 + x, x, y), -2))

    assert rf(x, m).is_integer is None
    assert rf(n, k).is_integer is None
    assert rf(n, m).is_integer is True
    assert rf(n, k + pi).is_integer is False
    assert rf(n, m + pi).is_integer is False
    assert rf(pi, m).is_integer is False

    assert rf(x, k).rewrite(ff) == ff(x + k - 1, k)
    assert rf(x, k).rewrite(binomial) == factorial(k)*binomial(x + k - 1, k)
    assert rf(n, k).rewrite(factorial) == \
        factorial(n + k - 1) / factorial(n - 1)

开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:52，代码来源:test_comb_factorials.py

示例10: test_rf_eval_apply

def test_rf_eval_apply():
    x, y = symbols('x,y')

    assert rf(nan, y) == nan

    assert rf(x, y) == rf(x, y)

    assert rf(oo, 0) == 1
    assert rf(-oo, 0) == 1

    assert rf(oo, 6) == oo
    assert rf(-oo, 7) == -oo

    assert rf(oo, -6) == oo
    assert rf(-oo, -7) == oo

    assert rf(x, 0) == 1
    assert rf(x, 1) == x
    assert rf(x, 2) == x*(x + 1)
    assert rf(x, 3) == x*(x + 1)*(x + 2)
    assert rf(x, 5) == x*(x + 1)*(x + 2)*(x + 3)*(x + 4)

    assert rf(x, -1) == 1/(x - 1)
    assert rf(x, -2) == 1/((x - 1)*(x - 2))
    assert rf(x, -3) == 1/((x - 1)*(x - 2)*(x - 3))

    assert rf(1, 100) == factorial(100)

开发者ID:FedericoV，项目名称:sympy，代码行数:27，代码来源:test_comb_factorials.py

示例11: test_rf_eval_apply

def test_rf_eval_apply():
    x, y = symbols('x,y')

    assert rf(nan, y) == nan

    assert rf(x, y) == rf(x, y)

    assert rf(oo, 0) == 1
    assert rf(-oo, 0) == 1

    assert rf(oo, 6) == oo
    assert rf(-oo, 7) == -oo

    assert rf(oo, -6) == oo
    assert rf(-oo, -7) == oo

    assert rf(x, 0) == 1
    assert rf(x, 1) == x
    assert rf(x, 2) == x*(x + 1)
    assert rf(x, 3) == x*(x + 1)*(x + 2)
    assert rf(x, 5) == x*(x + 1)*(x + 2)*(x + 3)*(x + 4)

    assert rf(x, -1) == 1/(x - 1)
    assert rf(x, -2) == 1/((x - 1)*(x - 2))
    assert rf(x, -3) == 1/((x - 1)*(x - 2)*(x - 3))

    assert rf(1, 100) == factorial(100)

    n = Symbol('n', integer=True)
    k = Symbol('k', integer=True)
    m = Symbol('m', integer=True, nonnegative=True)
    assert rf(x, m).is_integer is None
    assert rf(n, k).is_integer is None
    assert rf(n, m).is_integer is True
    assert rf(n, k + pi).is_integer is False
    assert rf(n, m + pi).is_integer is False
    assert rf(pi, m).is_integer is False

开发者ID:rahvar，项目名称:sympy，代码行数:37，代码来源:test_comb_factorials.py

示例12: to_sequence

    def to_sequence(self):
        """
        Finds the recurrence relation in power series expansion
        of the function.

        Examples
        ========

        >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators
        >>> from sympy.polys.domains import ZZ, QQ
        >>> from sympy import symbols
        >>> x = symbols('x')
        >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx')

        >>> HolonomicFunction(Dx - 1, x, 0, [1]).to_sequence()
        HolonomicSequence((-1) + (n + 1)Sn, n), u(0) = 1

        See Also
        ========

        HolonomicFunction.series

        References
        ==========

        hal.inria.fr/inria-00070025/document
        """

        dict1 = {}
        n = symbols('n', integer=True)
        dom = self.annihilator.parent.base.dom
        R, _ = RecurrenceOperators(dom.old_poly_ring(n), 'Sn')

        for i, j in enumerate(self.annihilator.listofpoly):
            listofdmp = j.all_coeffs()
            degree = len(listofdmp) - 1
            for k in range(degree + 1):
                coeff = listofdmp[degree - k]
                if coeff == 0:
                    continue
                if i - k in dict1:
                    dict1[i - k] += (coeff * rf(n - k + 1, i))
                else:
                    dict1[i - k] = (coeff * rf(n - k + 1, i))

        sol = []
        lower = min(dict1.keys())
        upper = max(dict1.keys())

        for j in range(lower, upper + 1):
            if j in dict1.keys():
                sol.append(dict1[j].subs(n, n - lower))
            else:
                sol.append(S(0))
        # recurrence relation
        sol = RecurrenceOperator(sol, R)

        if not self._have_init_cond:
            return HolonomicSequence(sol)
        if self.x0 != 0:
            return HolonomicSequence(sol)
        # computing the initial conditions for recurrence
        order = sol.order
        all_roots = roots(sol.listofpoly[-1].rep, filter='Z')
        all_roots = all_roots.keys()

        if all_roots:
            max_root = max(all_roots)
            if max_root >= 0:
                order += max_root + 1

        y0 = _extend_y0(self, order)
        u0 = []
        # u(n) = y^n(0)/factorial(n)
        for i, j in enumerate(y0):
            u0.append(j / factorial(i))

        return HolonomicSequence(sol, u0)

开发者ID:Carreau，项目名称:sympy，代码行数:78，代码来源:holonomic.py

示例13: test_rf_eval_apply

def test_rf_eval_apply():
    x, y = symbols("x,y")
    n, k = symbols("n k", integer=True)
    m = Symbol("m", integer=True, nonnegative=True)

    assert rf(nan, y) == nan
    assert rf(x, nan) == nan

    assert rf(x, y) == rf(x, y)

    assert rf(oo, 0) == 1
    assert rf(-oo, 0) == 1

    assert rf(oo, 6) == oo
    assert rf(-oo, 7) == -oo

    assert rf(oo, -6) == oo
    assert rf(-oo, -7) == oo

    assert rf(x, 0) == 1
    assert rf(x, 1) == x
    assert rf(x, 2) == x * (x + 1)
    assert rf(x, 3) == x * (x + 1) * (x + 2)
    assert rf(x, 5) == x * (x + 1) * (x + 2) * (x + 3) * (x + 4)

    assert rf(x, -1) == 1 / (x - 1)
    assert rf(x, -2) == 1 / ((x - 1) * (x - 2))
    assert rf(x, -3) == 1 / ((x - 1) * (x - 2) * (x - 3))

    assert rf(1, 100) == factorial(100)

    assert rf(x ** 2 + 3 * x, 2) == x ** 4 + 8 * x ** 3 + 19 * x ** 2 + 12 * x
    assert rf(x ** 3 + x, -2) == 1 / (x ** 6 - 9 * x ** 5 + 35 * x ** 4 - 75 * x ** 3 + 94 * x ** 2 - 66 * x + 20)

    assert rf(x, m).is_integer is None
    assert rf(n, k).is_integer is None
    assert rf(n, m).is_integer is True
    assert rf(n, k + pi).is_integer is False
    assert rf(n, m + pi).is_integer is False
    assert rf(pi, m).is_integer is False

    assert rf(x, k).rewrite(ff) == ff(x + k - 1, k)
    assert rf(x, k).rewrite(binomial) == factorial(k) * binomial(x + k - 1, k)
    assert rf(n, k).rewrite(factorial) == factorial(n + k - 1) / factorial(n - 1)

开发者ID:scopatz，项目名称:sympy，代码行数:44，代码来源:test_comb_factorials.py

示例14: test_F1

def test_F1():
    assert rf(x, 3) == x*(1 + x)*(2 + x)

开发者ID:batya239，项目名称:sympy，代码行数:2，代码来源:test_wester.py

示例15: test_rational_products

def test_rational_products():
    assert product(1 + 1/k, (k, 1, n)) == rf(2, n)/factorial(n)

开发者ID:A-turing-machine，项目名称:sympy，代码行数:2，代码来源:test_products.py

示例16: test_gammasimp

def test_gammasimp():
    R = Rational

    # was part of test_combsimp_gamma() in test_combsimp.py
    assert gammasimp(gamma(x)) == gamma(x)
    assert gammasimp(gamma(x + 1)/x) == gamma(x)
    assert gammasimp(gamma(x)/(x - 1)) == gamma(x - 1)
    assert gammasimp(x*gamma(x)) == gamma(x + 1)
    assert gammasimp((x + 1)*gamma(x + 1)) == gamma(x + 2)
    assert gammasimp(gamma(x + y)*(x + y)) == gamma(x + y + 1)
    assert gammasimp(x/gamma(x + 1)) == 1/gamma(x)
    assert gammasimp((x + 1)**2/gamma(x + 2)) == (x + 1)/gamma(x + 1)
    assert gammasimp(x*gamma(x) + gamma(x + 3)/(x + 2)) == \
        (x + 2)*gamma(x + 1)

    assert gammasimp(gamma(2*x)*x) == gamma(2*x + 1)/2
    assert gammasimp(gamma(2*x)/(x - S(1)/2)) == 2*gamma(2*x - 1)

    assert gammasimp(gamma(x)*gamma(1 - x)) == pi/sin(pi*x)
    assert gammasimp(gamma(x)*gamma(-x)) == -pi/(x*sin(pi*x))
    assert gammasimp(1/gamma(x + 3)/gamma(1 - x)) == \
        sin(pi*x)/(pi*x*(x + 1)*(x + 2))

    assert gammasimp(factorial(n + 2)) == gamma(n + 3)
    assert gammasimp(binomial(n, k)) == \
        gamma(n + 1)/(gamma(k + 1)*gamma(-k + n + 1))

    assert powsimp(gammasimp(
        gamma(x)*gamma(x + S(1)/2)*gamma(y)/gamma(x + y))) == \
        2**(-2*x + 1)*sqrt(pi)*gamma(2*x)*gamma(y)/gamma(x + y)
    assert gammasimp(1/gamma(x)/gamma(x - S(1)/3)/gamma(x + S(1)/3)) == \
        3**(3*x - S(3)/2)/(2*pi*gamma(3*x - 1))
    assert simplify(
        gamma(S(1)/2 + x/2)*gamma(1 + x/2)/gamma(1 + x)/sqrt(pi)*2**x) == 1
    assert gammasimp(gamma(S(-1)/4)*gamma(S(-3)/4)) == 16*sqrt(2)*pi/3

    assert powsimp(gammasimp(gamma(2*x)/gamma(x))) == \
        2**(2*x - 1)*gamma(x + S(1)/2)/sqrt(pi)

    # issue 6792
    e = (-gamma(k)*gamma(k + 2) + gamma(k + 1)**2)/gamma(k)**2
    assert gammasimp(e) == -k
    assert gammasimp(1/e) == -1/k
    e = (gamma(x) + gamma(x + 1))/gamma(x)
    assert gammasimp(e) == x + 1
    assert gammasimp(1/e) == 1/(x + 1)
    e = (gamma(x) + gamma(x + 2))*(gamma(x - 1) + gamma(x))/gamma(x)
    assert gammasimp(e) == (x**2 + x + 1)*gamma(x + 1)/(x - 1)
    e = (-gamma(k)*gamma(k + 2) + gamma(k + 1)**2)/gamma(k)**2
    assert gammasimp(e**2) == k**2
    assert gammasimp(e**2/gamma(k + 1)) == k/gamma(k)
    a = R(1, 2) + R(1, 3)
    b = a + R(1, 3)
    assert gammasimp(gamma(2*k)/gamma(k)*gamma(k + a)*gamma(k + b))
    3*2**(2*k + 1)*3**(-3*k - 2)*sqrt(pi)*gamma(3*k + R(3, 2))/2

    # issue 9699
    assert gammasimp((x + 1)*factorial(x)/gamma(y)) == gamma(x + 2)/gamma(y)
    assert gammasimp(rf(x + n, k)*binomial(n, k)) == gamma(n + 1)*gamma(k + n
        + x)/(gamma(k + 1)*gamma(n + x)*gamma(-k + n + 1))

    A, B = symbols('A B', commutative=False)
    assert gammasimp(e*B*A) == gammasimp(e)*B*A

    # check iteration
    assert gammasimp(gamma(2*k)/gamma(k)*gamma(-k - R(1, 2))) == (
        -2**(2*k + 1)*sqrt(pi)/(2*((2*k + 1)*cos(pi*k))))
    assert gammasimp(
        gamma(k)*gamma(k + R(1, 3))*gamma(k + R(2, 3))/gamma(3*k/2)) == (
        3*2**(3*k + 1)*3**(-3*k - S.Half)*sqrt(pi)*gamma(3*k/2 + S.Half)/2)

    # issue 6153
    assert gammasimp(gamma(S(1)/4)/gamma(S(5)/4)) == 4

    # was part of test_combsimp() in test_combsimp.py
    assert gammasimp(binomial(n + 2, k + S(1)/2)) == gamma(n + 3)/ \
        (gamma(k + S(3)/2)*gamma(-k + n + S(5)/2))
    assert gammasimp(binomial(n + 2, k + 2.0)) == \
        gamma(n + 3)/(gamma(k + 3.0)*gamma(-k + n + 1))

    # issue 11548
    assert gammasimp(binomial(0, x)) == sin(pi*x)/(pi*x)

    e = gamma(n + S(1)/3)*gamma(n + S(2)/3)
    assert gammasimp(e) == e
    assert gammasimp(gamma(4*n + S(1)/2)/gamma(2*n - S(3)/4)) == \
        2**(4*n - S(5)/2)*(8*n - 3)*gamma(2*n + S(3)/4)/sqrt(pi)

    i, m = symbols('i m', integer = True)
    e = gamma(exp(i))
    assert gammasimp(e) == e
    e = gamma(m + 3)
    assert gammasimp(e) == e
    e = gamma(m + 1)/(gamma(i + 1)*gamma(-i + m + 1))
    assert gammasimp(e) == e

    p = symbols("p", integer=True, positive=True)
    assert gammasimp(gamma(-p+4)) == gamma(-p+4)

开发者ID:asmeurer，项目名称:sympy，代码行数:98，代码来源:test_gammasimp.py

示例17: Symbol

n = Symbol("n", positive=True, integer=True)
k = Symbol("k", integer=True)
# binomialpoly = implemented_function(Function('(x+y)^n'), lambda n: (x+y)**n)
# binomialpoly_n = lambdify(n, binomialpoly(n))
binomialpoly = (x + y) ** n
binomialpolyexpand = Sum(binomial(n, k) * x ** k * y ** (n - k), (k, 0, n))

binomialpoly.subs(n, 1) == binomialpolyexpand.subs(n, 1).doit()  # True
binomialpoly.subs(n, 2).expand() == binomialpolyexpand.subs(n, 2).doit()  # True
binomialpoly.subs(n, 3).expand() == binomialpolyexpand.subs(n, 3).doit()  # True
binomialpoly.subs(n, 4).expand() == binomialpolyexpand.subs(n, 4).doit()  # True

# rising factorial
a, q = symbols("a q")
# a_n = Product(a+k,(k,0,n-1))
a_n = rf(a, n)
aq_n = Product(Rat(1) - a * q ** k, (k, 0, n - 1))
# e.g. aq_n.subs(n,3).doit()

# Hermite polynomials

HermiteF = factorial(n) * (Rat(-1)) ** k * (Rat(2) * x) ** (n - Rat(2) * k) / (factorial(n - Rat(2) * k) * factorial(k))
HermiteP = Sum(HermiteF, (k, 0, floor(n / 2)))
hermite_poly(1, x) == HermiteP.subs(n, 1).doit()  # True
hermite_poly(2, x) == HermiteP.subs(n, 2).doit()  # True
hermite_poly(3, x) == HermiteP.subs(n, 3).doit()  # True
hermite_poly(4, x) == HermiteP.subs(n, 4).doit()  # True

(HermiteF.subs(n, n + 1) / HermiteF).simplify()  # 2*x*(n + 1)/(-2*k + n + 1)
(HermiteF.subs(k, k + 1) / HermiteF).simplify()  # -(2*k - n)*(2*k - n + 1)/(4*x**2*(k + 1))

开发者ID:ernestyalumni，项目名称:qSApoly，代码行数:30，代码来源:hypergeo.py

注：本文中的sympy.rf函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。

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Python sympy.rf函数代码示例

示例1: test_special_products

示例2: test_rf_ff_eval_hiprec

示例3: test_rf_lambdify_mpmath

示例4: test_issue_9699

示例5: test_simple_products

示例6: test_ff_eval_apply

示例7: test_simple_products

示例8: test_rsolve_hyper

示例9: test_rf_eval_apply

示例10: test_rf_eval_apply

示例11: test_rf_eval_apply

示例12: to_sequence

示例13: test_rf_eval_apply

示例14: test_F1

示例15: test_rational_products

示例16: test_gammasimp

示例17: Symbol

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