Abel's method on summation by parts and hypergeometric series

Abstract

Hypergeometric series identities are revisited systematically by means of Abel's method on summation by parts. Several new formulae and transformations are also established. The author is convinced that Abel's method on summation by parts is a natural choice in dealing with classical hypergeometric series.

Keywords:

• Abel's lemma
• Finite difference
• Hypergeometric series

2000 Mathematics Subject Classification:

• Primary 33C20
• Secondary 05A19

Notes

^‡Current Address: Dipartimento di Matematica, Università degli Studi di Lecce, Lecce-Arnesano P. O. Box 193 73100 Lecce, Italia. Tel.: [phone]. Fax: [phone]. Email: [email protected]

This work is carried out during my visit to Dalian University of Technology (2005).

Additional information

Notes on contributors

Chu Wenchang

‡ ‡Current Address: Dipartimento di Matematica, Università degli Studi di Lecce, Lecce-Arnesano P. O. Box 193 73100 Lecce, Italia. Tel.: [phone]. Fax: [phone]. Email: [email protected]