A challenging test for convergence accelerators: summation of a series with a special sign pattern.
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Sidi, Avram (2006)
Applied Mathematics E-Notes [electronic only]
Roberto Barrio (1998)
Extracta Mathematicae
He, Tian-Xiao (2008)
Journal of Integer Sequences [electronic only]
A.A.M. Cuyt (1983)
Numerische Mathematik
Paul Wild (1987)
Numerische Mathematik
J.P. Delahaye (1980)
Numerische Mathematik
M. Mori (1980)
Numerische Mathematik
J. Della Dora, C. Di Crescenzo (1984)
Numerische Mathematik
J. Della Dora, C. Di Crescenzo (1984)
Numerische Mathematik
B. Germain-Bonne (1973)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Claude Brezinski (1985)
Numerische Mathematik
Cohen, Henri, Rodriguez Villegas, Fernando, Zagier, Don (2000)
Experimental Mathematics
C. Brezinski (1977/1978)
Numerische Mathematik
Yuri Melnikov (2010)
Open Mathematics
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...
A.N. Stokes (1983)
Numerische Mathematik
Krystyna Ziętak (1988)
Applicationes Mathematicae
Livne, Oren E., Wright, Grady B. (2006)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
C. Brezinski (1974/1975)
Numerische Mathematik
Donald R. Snow (1978)
Aequationes mathematicae
David Brink (2015)
Acta Arithmetica
We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula with convergence as , in much the same way as the Euler transformation gives with convergence as . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in the Appendix....
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