Abstract
Here proposed is a numerical method for distinguishing some divergent series from conver- gent ones. It is applicable to numerical integration of some functions over finite domains by iterative application of trapezoidal formula, as well as to some basic series in higher education, such as the harmonic series, ordinary Dirichlet series, and so on.
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References
Henrichi, P. (1974). Applied and Computational Complex Analysis, vol. 1, Wiley-Interscience.
Hitotumatu, S. (1973). Electronic Computers and Numerical Computations (in Japanese), Asakura-Shoten.
Koenig, J. (1884). Uber eine Eigenschaft der Potenzreihen, Mathematical Annalen, vol. 23, pp. 447–449.
Wynn, P. (1956). On a device for computing the em(Sm) Transformation, Mathematical Tables and other Aids to Computation, vol. 10, pp. 91–96.
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Nozaki, A. How to Detect Divergence of Some Series with Positive Terms. Behaviormetrika 15, 51–56 (1988). https://doi.org/10.2333/bhmk.15.23_51
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DOI: https://doi.org/10.2333/bhmk.15.23_51