Convergence acceleration of series through a variational approach

Details Convergence acceleration of series through a variational approach Convergence acceleration of series through a variational approach

2004-08-24

arxiv.org/abs/math-ph/0408036v4

Journal of Mathematical Analysis and Applications 323 (2006) 63-77

Physics

Mathematical Physics

19 pages, 9 figures, 1 table Accepted for publication on the Journal of Mathematical Analysis and Applications

Scientific paper

By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar exponentially convergent series for a large class of mathematical functions.

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