Some transformations of monotone sequences
HTML articles powered by AMS MathViewer
- by Jet Wimp PDF
- Math. Comp. 26 (1972), 251-254 Request permission
Abstract:
In this paper, we discuss a class of methods for summing sequences which are generalizations of a method due to Salzer. The methods are not regular, and in contrast to the classical regular methods, seem to work best on sequences which are monotone. In our main theorem, we determine a class of convergent sequences for which the methods yield sequences which converge to the same sum.References
- Herbert E. Salzer, A simple method for summing certain slowly convergent series, J. Math. and Phys. 33 (1955), 356–359. MR 68315, DOI 10.1002/sapm1954331356
- Herbert E. Salzer, Formulas for the partial summation of series, Math. Tables Aids Comput. 10 (1956), 149–156. MR 81528, DOI 10.1090/S0025-5718-1956-0081528-5
- Herbert E. Salzer and Genevieve M. Kimbro, Improved formulas for complete and partial summation of certain series, Math. Comp. 15 (1961), 23–39. MR 121972, DOI 10.1090/S0025-5718-1961-0121972-2 N. E. Nörlund, Vorlesungen über die Differenzenrechnung, Springer, Berlin, 1924; reprint, Chelsea, New York, 1954.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 251-254
- MSC: Primary 65B10
- DOI: https://doi.org/10.1090/S0025-5718-1972-0303674-X
- MathSciNet review: 0303674