In this coordinate system, the complete solution to the Helmholtz differential equation is a linear combination of half-integral order Bessel functions of the first and second kinds.
In this coordinate system, the complete solution to the Helmholtz differential equation is a linear combination of half-integral order Bessel functions of the first and second kinds. Solving Laplace's equation in this coordinate system yields an orthonormal set of functions proportional to the Legendre polynomials; those functions are known as this system's namesake harmonics. This coordinate system gives the natural definition of the solid angle as the double integral of sin phi d-theta d-phi, and only one of its three coordinates has dimensions of distance. For 10 points, identify this coordinate system in which coordinates are given by a polar angle, an azimuth, and a radius, such that points of constant radius form a ball.
In this coordinate system, the complete solution to the Helmholtz differential equation is a linear combination of half-integral order Bessel functions of the first and second kinds.
spherical coordinates