Generalizing from spheres to
spheroids with an axial semiaxis a (i.e., the semiaxis of revolution) and equatorial semiaxes b, the intrinsic viscosity can be written : \left[ \eta \right] = \left( \frac{4}{15} \right) (J + K - L) + \left( \frac{2}{3} \right) L + \left( \frac{1}{3} \right) M + \left( \frac{1}{15} \right) N where the constants are defined : M \ \stackrel{\mathrm{def}}{=}\ \frac{1}{a b^{4}} \frac{1}{J_{\alpha}^{\prime}} : K \ \stackrel{\mathrm{def}}{=}\ \frac{M}{2} : J \ \stackrel{\mathrm{def}}{=}\ K \frac{J_{\alpha}^{\prime\prime}}{J_{\beta}^{\prime\prime}} : L \ \stackrel{\mathrm{def}}{=}\ \frac{2}{a b^{2} \left( a^{2} + b^{2} \right)} \frac{1}{J_{\beta}^{\prime}} : N \ \stackrel{\mathrm{def}}{=}\ \frac{6}{a b^{2}} \frac{\left( a^{2} - b^{2} \right)}{a^{2} J_{\alpha} + b^{2} J_{\beta}} The J coefficients are the
Jeffery functions : J_{\alpha} = \int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right) \sqrt{\left( x + a^{2} \right)^{3}}} : J_{\beta} = \int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right)^{2} \sqrt{\left( x + a^{2} \right)}} : J_{\alpha}^{\prime} = \int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right)^{3} \sqrt{\left( x + a^{2} \right)}} : J_{\beta}^{\prime} = \int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right)^{2} \sqrt{\left( x + a^{2} \right)^{3}}} : J_{\alpha}^{\prime\prime} = \int_{0}^{\infty} \frac{x\ dx}{\left( x + b^{2} \right)^{3} \sqrt{\left( x + a^{2} \right)}} : J_{\beta}^{\prime\prime} = \int_{0}^{\infty} \frac{x\ dx}{\left( x + b^{2} \right)^{2} \sqrt{\left( x + a^{2} \right)^{3}}} ==General ellipsoidal formulae==