Extremal non-compactness of composition operators with linear fractional symbol

We realize the norms of certain composition operators Cφ with linear fractional symbol acting on the Hardy space in terms of the roots of associated hypergeometric functions. This realization leads to simple necessary and sufficient conditions on φ for Cφ to exhibit extremal non-compactness, establishes equivalence of cohyponormality and cosubnormality of composition operators with linear fractional symbol, and yields a complete classification of those linear fractional φ that induce composition operators whose norms are determined by the action of the adjoint on the normalized reproducing kernels in H2.