Abel's method on summation by parts and hypergeometric contiguous relations
Titel:
Abel's method on summation by parts and hypergeometric contiguous relations
Auteur:
Chu, Wenchang Wang, Xiaoxia
Verschenen in:
Integral transforms and special functions
Paginering:
Jaargang 18 (2007) nr. 11 pagina's 771-807
Jaar:
2007-01
Inhoud:
The modified Abel lemma on summation by parts is employed to investigate contiguous relations of classical hypergeometric 3F2-series. Several known and new two- and three-term relations are established. Inspired by the recent work due to Krattenthaler and Rivoal [Krattenthaler, C. and Rivoal, T., 2006, How can we escape Thomae's relations. Journal of Mathematical Society of Japan, 58, 183-210.], we shall construct further counter-examples to the conjecture made by Rhin and Viola [Rhin, G. and Viola, C. 2001, The group structure for ζ3. Acta Arithmatica, 97(3), 269-293.], which claims that two linearly dependent 3F2(1)-series of irrational values over satisfy one of Thomae's relations.
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