A Use of Symmetry: Generalization of an Integral Identity Found by M. L. Glasser

Abstract

The integral identity found by M. L. Glasser [3] is generalized using the permutation symmetry of coordinates of an n-spherical surface simplex. The first calculation technique is simple to apply, but the second technique allows further generalization of M. L. Glasser's identity. Analogous results are discussed for the n-hemispherical surface of the unit n-sphere and for the entire surface of the n-sphere. The n-sphere surface result is used to generalize M. L. Glasser's solution to a problem proposed by J. R. Bottiger [2].