Nonterminating well–poised hypergeometric series

Abstract

Two classes of nonterminating well--poised series are examined by means of the modified Abel lemma on summation by parts, that leads to several summation and transformation formulae.

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Keywords

• Classical hypergeometric series
• Abel's lemma on summation by parts
• Pfaff–Saalschütz theorem
• Dougall's formulae for $_2H_2$-series and $_5H_5$-series

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