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)"