Abstract
UDC 517.5
By means of the extended Gould–Hsu inverse series relations, we find that the dual relation of Dougall's summation theorem for the well-poised
7
F
6
-series can be used to construct numerous interesting Ramanujan-like infinite-series expressions for
π
±
1
and
π
±
2
,
including an elegant formula for
π
-2
due to Guillera.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
Reference34 articles.
1. V. Adamchik, S. Wagon, $pi$: A 2000-year search changes direction, Math. Educ. and Res., 5, № 1, 11–19 (1996).
2. D. Bailey et al., On the rapid computation of various polylogarithmic constants, Math. Comp., 66, № 218, 903–913 (1997).
3. W. N. Bailey, Generalized hypergeometric series, Cambridge Univ. Press, Cambridge (1935).
4. D.~M.~Bressoud, A matrix inverse, Proc. Amer. Math. Soc., 88, № 3, 446–448 (1983).
5. Yu.~A.~Brychkov, Handbook of special functions: derivatives, integrals, series and other formulas, CRC Press, Boca Raton, FL (2008).