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)
def test_integral_transforms():
x = Symbol("x")
k = Symbol("k")
f = Function("f")
a = Symbol("a")
b = Symbol("b")
assert latex(
MellinTransform(f(x), x, k)
) == r"\mathcal{M}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseMellinTransform(f(k), k, x, a, b)
) == r"\mathcal{M}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
LaplaceTransform(f(x), x, k)
) == r"\mathcal{L}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseLaplaceTransform(f(k), k, x, (a, b))
) == r"\mathcal{L}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
FourierTransform(f(x), x, k)
) == r"\mathcal{F}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseFourierTransform(f(k), k, x)
) == r"\mathcal{F}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
CosineTransform(f(x), x, k)
) == r"\mathcal{COS}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseCosineTransform(f(k), k, x)
) == r"\mathcal{COS}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
SineTransform(f(x), x, k)
) == r"\mathcal{SIN}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseSineTransform(f(k), k, x)
) == r"\mathcal{SIN}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
