k0 2*pi*freq/c0 Wavenumber
kR k0*R0 k*R
r sqrt(x^2+y^2+z^2) "Distance to (x,y,z)"
ryz sqrt(y^2+z^2) "Distance in yz-plane"
phi atan2(ryz,x) "Polar angle"
n 1 "Initialization of summation"
dJ d(J(n,kR),kR) "Derivative of spherical Bessel function (of the first kind)"
dN d(N(n,kR),kR) "Derivative of spherical Bessel function (of the second kind)"
dH d(J(n,kR),kR)+i*d(N(n,kR),kR) "Derivative of spherical Hankel function"
H J(n,k0*r)+i*N(n,k0*r) "Spherical Hankel function"
pana conj(sum(-i^n*(2*n+1)*dJ/dH*legendre(n,cos(phi))*H,n,0,100)) "Scattered pressure analytical expression"