Hypergeometric series and the Riemann zeta function

Wenchang Chu

Acta Arithmetica (1997)

  • Volume: 82, Issue: 2, page 103-118
  • ISSN: 0065-1036

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Wenchang Chu. "Hypergeometric series and the Riemann zeta function." Acta Arithmetica 82.2 (1997): 103-118. <http://eudml.org/doc/207083>.

@article{WenchangChu1997,
author = {Wenchang Chu},
journal = {Acta Arithmetica},
keywords = {the Riemann zeta function; the harmonic numbers; hypergeometric series; the gamma function; symmetric functions; infinite series identities; Riemann zeta-function},
language = {eng},
number = {2},
pages = {103-118},
title = {Hypergeometric series and the Riemann zeta function},
url = {http://eudml.org/doc/207083},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Wenchang Chu
TI - Hypergeometric series and the Riemann zeta function
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 2
SP - 103
EP - 118
LA - eng
KW - the Riemann zeta function; the harmonic numbers; hypergeometric series; the gamma function; symmetric functions; infinite series identities; Riemann zeta-function
UR - http://eudml.org/doc/207083
ER -

References

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  1. [1] B. C. Berndt, Ramanujan's Notebooks, Part I, Springer, New York, 1985. Zbl0555.10001
  2. [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. Zbl0840.11036
  3. [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. Zbl0830.05006
  4. [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. Zbl0782.33001
  5. [5] Y. L. Luke, The Special Functions and Their Approximations, Academic Press, London, 1969. Zbl0193.01701
  6. [6] I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Univ. Press, London, 1979. Zbl0487.20007
  7. [7] L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. Zbl0135.28101

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