UPON THE PADE TABLE DERIVED FROM A STIELTJES SERIES.

Abstract

The paper is concerned with the Pade table constructed from a series Summation, s = 0 to s = infinity, of ((-1) to the s power (c subscript s) (z superscript s)) whose coefficients are given by c subscript s = the integral from 0 to infinity of the quantity (u to the s power) d psi (u), where psi (u) is a bounded non-decreasing function in 0 = or < u = or < infinity. It is shown that under certain conditions, when z is real and positive, the Pade quotients along both forward and backward diagonals from monotonic sequences; an optimal property of the quotients lying upon the principal diagonal is proved. Some new convergence results are derived. The Pade quotients are compared with the transformed sums produced by certain linear methods. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0657573

Entities

People

  • P. Wynn

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Convergence
  • Integrals
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis