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