def test_hankel_transform():
from diofant import gamma, sqrt, exp
r = Symbol("r")
k = Symbol("k")
nu = Symbol("nu")
m = Symbol("m")
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)
assert inverse_hankel_transform(
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) == \
2**(nu + 1)*a*k**(-nu - 3)*(a**2/k**2 + 1)**(-nu -
Rational(3, 2))*gamma(nu + Rational(3, 2))/sqrt(pi)
assert inverse_hankel_transform(
2**(nu + 1) * a * k**(-nu - 3) *
(a**2 / k**2 + 1)**(-nu - Rational(3, 2)) *
gamma(nu + Rational(3, 2)) / sqrt(pi), k, r, nu) == r**nu * exp(-a * r)
def test_hankel_transform():
r = Symbol("r")
k = Symbol("k")
nu = Symbol("nu")
m = Symbol("m")
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)
assert inverse_hankel_transform(
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) == \
2**(nu + 1)*a*k**(-nu - 3)*(a**2/k**2 + 1)**(-nu -
Rational(3, 2))*gamma(nu + Rational(3, 2))/sqrt(pi)
assert inverse_hankel_transform(
2**(nu + 1)*a*k**(-nu - 3)*(a**2/k**2 + 1)**(-nu - Rational(3, 2))*gamma(
nu + Rational(3, 2))/sqrt(pi), k, r, nu) == r**nu*exp(-a*r)