UPON THE PADE TABLE DERIVED FROM A STIELTJES SERIES.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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
- Numerical Mathematics