本文整理汇总了Python中sympy.integrals.transforms.mellin_transform函数的典型用法代码示例。如果您正苦于以下问题：Python mellin_transform函数的具体用法？Python mellin_transform怎么用？Python mellin_transform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mellin_transform函数的6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，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: test_undefined_function
def test_undefined_function():
from sympy import Function, MellinTransform
f = Function('f')
assert mellin_transform(f(x), x, s) == MellinTransform(f(x), x, s)
assert mellin_transform(f(x) + exp(-x), x, s) == \
(MellinTransform(f(x), x, s) + gamma(s), (0, oo), True)
assert laplace_transform(2*f(x), x, s) == 2*LaplaceTransform(f(x), x, s)示例2: test_expint
def test_expint():
from sympy import E1, expint, Max, re, lerchphi, Symbol, simplify, Si, Ci, Ei
aneg = Symbol("a", negative=True)
u = Symbol("u", polar=True)
assert mellin_transform(E1(x), x, s) == (gamma(s) / s, (0, oo), True)
assert inverse_mellin_transform(gamma(s) / s, s, x, (0, oo)).rewrite(expint).expand() == E1(x)
assert mellin_transform(expint(a, x), x, s) == (gamma(s) / (a + s - 1), (Max(1 - re(a), 0), oo), True)
# XXX IMT has hickups with complicated strips ...
assert simplify(
unpolarify(
inverse_mellin_transform(gamma(s) / (aneg + s - 1), s, x, (1 - aneg, oo)).rewrite(expint).expand(func=True)
)
) == expint(aneg, x)
assert mellin_transform(Si(x), x, s) == (
-2 ** s * sqrt(pi) * gamma(s / 2 + S(1) / 2) / (2 * s * gamma(-s / 2 + 1)),
(-1, 0),
True,
)
assert inverse_mellin_transform(
-2 ** s * sqrt(pi) * gamma((s + 1) / 2) / (2 * s * gamma(-s / 2 + 1)), s, x, (-1, 0)
) == Si(x)
assert mellin_transform(Ci(sqrt(x)), x, s) == (
-2 ** (2 * s - 1) * sqrt(pi) * gamma(s) / (s * gamma(-s + S(1) / 2)),
(0, 1),
True,
)
assert inverse_mellin_transform(
-4 ** s * sqrt(pi) * gamma(s) / (2 * s * gamma(-s + S(1) / 2)), s, u, (0, 1)
).expand() == Ci(sqrt(u))
# TODO LT of Si, Shi, Chi is a mess ...
assert laplace_transform(Ci(x), x, s) == (-log(1 + s ** 2) / 2 / s, 0, True)
assert laplace_transform(expint(a, x), x, s) == (lerchphi(s * polar_lift(-1), 1, a), 0, S(0) < re(a))
assert laplace_transform(expint(1, x), x, s) == (log(s + 1) / s, 0, True)
assert laplace_transform(expint(2, x), x, s) == ((s - log(s + 1)) / s ** 2, 0, True)
assert inverse_laplace_transform(-log(1 + s ** 2) / 2 / s, s, u).expand() == Heaviside(u) * Ci(u)
assert inverse_laplace_transform(log(s + 1) / s, s, x).rewrite(expint) == Heaviside(x) * E1(x)
assert (
inverse_laplace_transform((s - log(s + 1)) / s ** 2, s, x).rewrite(expint).expand()
== (expint(2, x) * Heaviside(x)).rewrite(Ei).rewrite(expint).expand()
)示例3: test_as_integral
def test_as_integral():
from sympy import Function, Integral
f = Function('f')
assert mellin_transform(f(x), x, s).rewrite('Integral') == \
Integral(x**(s - 1)*f(x), (x, 0, oo))
assert fourier_transform(f(x), x, s).rewrite('Integral') == \
Integral(f(x)*exp(-2*I*pi*s*x), (x, -oo, oo))
assert laplace_transform(f(x), x, s).rewrite('Integral') == \
Integral(f(x)*exp(-s*x), (x, 0, oo))
assert str(inverse_mellin_transform(f(s), s, x, (a, b)).rewrite('Integral')) \
== "Integral(x**(-s)*f(s), (s, _c - oo*I, _c + oo*I))"
assert str(inverse_laplace_transform(f(s), s, x).rewrite('Integral')) == \
"Integral(f(s)*exp(s*x), (s, _c - oo*I, _c + oo*I))"
assert inverse_fourier_transform(f(s), s, x).rewrite('Integral') == \
Integral(f(s)*exp(2*I*pi*s*x), (s, -oo, oo))示例4: test_free_symbols
def test_free_symbols():
from sympy import Function
f = Function('f')
assert mellin_transform(f(x), x, s).free_symbols == set([s])
assert mellin_transform(f(x)*a, x, s).free_symbols == set([s, a])示例5: test_issue_7181
def test_issue_7181():
assert mellin_transform(1 / (1 - x), x, s) != None示例6: test_as_integral
def test_as_integral():
from sympy import Function, Integral
f = Function('f')
assert mellin_transform(f(x), x, s).rewrite('Integral') == \
Integral(x**(s - 1)*f(x), (x, 0, oo))