This paper presents theoretical analysis and software implementation for real harmonics on the special orthogonal group. Noncommutative harmonic complex-valued functions group has been studied extensively. However, it is customary to treat as a case of complex analysis, there have limited results developed specifically real-valued functions. Here, we develop set explicit formulas irreducible un...

We study the integrals of type I(a) = ∫ On ∏ u aij ij du, depending on a matrix a ∈Mp×q(N), whose exact computation is an open problem. Our results are as follows: (1) an extension of the “elementary expansion” formula from the case a ∈M2×q(2N) to the general case a ∈Mp×q(N), (2) the construction of the “best algebraic normalization” of I(a), in the case a ∈M2×q(N), (3) an explicit formula for ...