In eq. (10.35) of his book "Symmetric functions and Hall polynomials" I.G.Macdonald gives the following scalar product, under which Jack polynomials with different partitions $\mu\neq\lambda$ are orthogonal

$$\langle J^\alpha_\lambda(z_1,z_2),J^\alpha_\mu(z_1,z_2)\rangle'_2=\frac{1}{2}\int_T J^\alpha_\lambda(z_1,z_2)\overline{J^\alpha_\mu(z_1,z_2)}\prod_{i\neq j}\left(1-\frac{z_i}{z_j}\right)^{1/\alpha}dz^2$$

where the integration contour is $T=\{(z_1,z_2)\in\mathbb{C}^2:|z_1|=1,|z_2|=1\}$. Therefore, the integral equals $c_{\lambda,\alpha}\delta_{\mu,\lambda}$. However, Macdonald does not give the normalization $c_{\lambda,\alpha}$ for the scalar product. Is the normalization known?