An alternative representation for the parity-projected Wigner dj(β) rotation matrix is derived as the product of two triangular matrices composed of Gegenbauer polynomials with negative and positive upper indices, respectively. We relate this representation for dj(β) to the one presented by Matveenko [Phys. Rev. A 59, 1034 (1999)], which, in contrast with our result, requires for its evaluation a matrix inversion. In addition, identities for bilinear sums of Gegenbauer polynomials are derived. This work is based on our recently introduced invariant representations for finite rotation matrices [Phys. Rev. A 57, 3233 (1998)]
