Hypergeometric series and the Riemann zeta function

ArticleOriginal scientific text

Title

Authors ¹

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

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

B. C. Berndt, Ramanujan's Notebooks, Part I, Springer, New York, 1985.
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.
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.
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.
Y. L. Luke, The Special Functions and Their Approximations, Academic Press, London, 1969.
I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Univ. Press, London, 1979.
L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966.