Inversion techniques and combinatorial identities: a unified treatment for the 7F6 series identities
- Autores: Chu Wenchang
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 45, Fasc. 1, 1994, págs. 13-44
- Idioma: inglés
- Enlaces
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Resumen
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.
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