Associated Legendre Functions and Spherical Harmonics of Fractional Degree and Order
Associated Legendre Functions and Spherical Harmonics of Fractional Degree and Order
Trigonometric formulas are derived for certain families of associated Legendre functions of fractional degree and order, for use in approximation theory. These functions are algebraic, and when viewed as Gauss hypergeometric functions, belong to types classified by Schwarz, with dihedral, tetrahedral, or octahedral monodromy. The dihedral Legendre functions are expressed …