Hypergeometric series and the Riemann zeta function

• Autorzy: Wenchang Chu
• Języki publikacji: EN

Słowa kluczowe

EN

the Riemann zeta function   the harmonic numbers   hypergeometric series   the gamma function   symmetric functions  

Kategorie tematyczne

• 11M06: ζ ( s ) and L ( s , χ )
• 33C20: Generalized hypergeometric series, p F q

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 2
• Strony: 103-118

Daty

wydano

1997

otrzymano

1996-04-02

poprawiono

1997-03-25

Twórcy

autor

Wenchang Chu

• Istituto di Matematica "Guido Castelnuovo", Università degli Studi di Roma "La Sapienza", 00185 Roma, Italy

Bibliografia

• [1] B. C. Berndt, Ramanujan's Notebooks, Part I, Springer, New York, 1985.
• [2] D. Borwein and J. M. Borwein, On an intriguing integral and some series related to ζ(4), Proc. Amer. Math. Soc. 123 (1995), 1191-1198.
• [3] W. Chu, Inversion techniques and combinatorial identities: A quick introduction to hypergeometric evaluations, in: Runs and Patterns in Probability: Selected Papers, A. P. Godbole and S. G. Papastavridis (eds.), Math. Appl. 283, Kluwer, Dordrecht, 1994, 31-57.
• [4] P. J. De Doelder, On some series containing ψ(x)-ψ(y) and (ψ(x)-ψ(y))² for certain values of x and y, J. Comput. Appl. Math. 37 (1991), 125-141.
• [5] Y. L. Luke, The Special Functions and Their Approximations, Academic Press, London, 1969.
• [6] I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Univ. Press, London, 1979.
• [7] L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966.