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The product of three hypergeometric series of type ₀ F₁ with arguments x, x, ² x (= third root of unity) is expressed as a single hypergeometric series of type ₂ F₇. The proof uses differential equations; the basic idea (elimination of irreducible terms by means of the Cayley-Hamilton theorem) is more generally applicable.
Peter Henrici (Sun,) studied this question.