We realize the norms of certain composition operators C ϕ 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 C ϕ 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 C * ϕ on the normalized reproducing kernels in H 2 .

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