Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Some transformations of monotone sequences


Author: Jet Wimp
Journal: Math. Comp. 26 (1972), 251-254
MSC: Primary 65B10
DOI: https://doi.org/10.1090/S0025-5718-1972-0303674-X
MathSciNet review: 0303674
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] H. E. Salzer, ``A simple method for summing certain slowly convergent series,'' J. Math. Physics, v. 33, 1955, pp. 356-359. MR 16, 863. MR 0068315 (16:863d)
  • [2] H. E. Salzer, ``Formulas for the partial summation of series,'' MTAC, v. 10, 1956, pp. 149-156. MR 18, 416. MR 0081528 (18:416a)
  • [3] H. E. Salzer & G. M. Kimbro, ``Improved formulas for complete and partial summation of certain series,'' Math. Comp., v. 15, 1961, pp. 23-39. MR 22 #12699. MR 0121972 (22:12699)
  • [4] N. E. Nörlund, Vorlesungen über die Differenzenrechnung, Springer, Berlin, 1924; reprint, Chelsea, New York, 1954.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65B10

Retrieve articles in all journals with MSC: 65B10


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0303674-X
Keywords: Monotone sequences, summation methods, psi function
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society