CALCULATION OF ASSOCIATED LEGENDRE POLYNOMIALS WITH NON-INTEGER DEGREE - D. Trott, Keith (Applied Computational Electromagnetics Society Journal (ACES), 2022)
The exact eigenfunction solution for the electromagnetic scattering from a perfectly conducting cone (or any other sectoral body of revolution with a tip) requires the solution in the form of spherical harmonics. The solution for the variation of these harmonics is the associated Legendre polynomial. The boundary conditions for the cone generate associated Legendre polynomials with non-integer degree found for a specific cone angle. This paper will discuss the derivation used to calculate the associated Legendre polynomial, the determination of the eigenvalues, the incomplete normalization integral, and a validation technique. [Vol. 11, No. 1 (1996), pp 85-89, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]