text: In physics, the plane-wave expansion expresses a plane wave as a linear combination of spherical waves:
  where
  *  is the imaginary unit,
  *  is a wave vector of length ,
  *  is a position vector of length ,
  *  are spherical Bessel functions,
  *  are Legendre polynomials, and
  * the hat  denotes the unit vector.
  In the special case where  is aligned with the z axis,
  where  is the spherical polar angle of .