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# sympy.integrals.transforms.hankel_transform

All Samples(10)  |  Call(8)  |  Derive(0)  |  Import(2)

from sympy.integrals.transforms import (mellin_transform,
inverse_mellin_transform, laplace_transform, inverse_laplace_transform,
fourier_transform, inverse_fourier_transform,
sine_transform, inverse_sine_transform,
cosine_transform, inverse_cosine_transform,
a = symbols("a")

assert hankel_transform(1/r, r, k, 0) == 1/k
assert inverse_hankel_transform(1/k, k, r, 0) == 1/r

assert hankel_transform(
1/r**m, r, k, 0) == 2**(-m + 1)*k**(m - 2)*gamma(-m/2 + 1)/gamma(m/2)
2**(-m + 1)*k**(m - 2)*gamma(-m/2 + 1)/gamma(m/2), k, r, 0) == r**(-m)

assert hankel_transform(1/r**m, r, k, nu) == (
2*2**(-m)*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2))
assert inverse_hankel_transform(2**(-m + 1)*k**(
m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2), k, r, nu) == r**(-m)

assert hankel_transform(r**nu*exp(-a*r), r, k, nu) == \

from sympy.integrals.transforms import (mellin_transform,
inverse_mellin_transform, laplace_transform, inverse_laplace_transform,
fourier_transform, inverse_fourier_transform,
sine_transform, inverse_sine_transform,
cosine_transform, inverse_cosine_transform,
a = symbols("a")

assert hankel_transform(1/r, r, k, 0) == 1/k
assert inverse_hankel_transform(1/k, k, r, 0) == 1/r

assert hankel_transform(
1/r**m, r, k, 0) == 2**(-m + 1)*k**(m - 2)*gamma(-m/2 + 1)/gamma(m/2)
2**(-m + 1)*k**(m - 2)*gamma(-m/2 + 1)/gamma(m/2), k, r, 0) == r**(-m)

assert hankel_transform(1/r**m, r, k, nu) == (
2*2**(-m)*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2))
assert inverse_hankel_transform(2**(-m + 1)*k**(
m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2), k, r, nu) == r**(-m)

assert hankel_transform(r**nu*exp(-a*r), r, k, nu) == \