Spherical Harmonics in p Dimensions
  The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before beginning the main subject matter. The reader is assumed to have knowledge of multivariable calculus and linear algebra as well as some level of comfort with reading proofs. 
Christopher Frye, Costas J. Efthimiou
math.CA hep-th math-ph math.AP math.MP