Conical function

The cones are special functions spherical functions, which were introduced by Gustav Ferdinand Mehler in 1868 as a solution to the problem of determination of the potential of distributed on a conical surface electric charges.

Definition

Originally introduced by Mehler functions can be represented by spherical harmonics, namely associated Legendre polynomials of first and second kind with a special complex index:

It is real and arbitrary. According to today, these two special Legendrefunktionen are called cone functions. Especially true with and: