Resumen de Inversion techniques and combinatorial identities: a unified treatment for the 7F6 series identities

Chu Wenchang

• As an extension of a useful inverse pair due to Gould–Hsu (1973), a general pair of reciprocal relations is established. The inversion technique for proving combinatorial identities, originated by Riordan (1968) and Greene & Knuth (1981), is developed systematically to explore the dual relations of Pfaff–Saalschutz and Dougall–Dixon formulae. Most of the known strange hypergeometric evaluations, covered in Bailey (1935), Slater (1966), Gessel & Staton (1982), Gasper (1989) and Gasper & Rahman (1990), and several new mysterious looking formulas are demonstrated almost mechanically.