The Hankel power sum matrix inverse and the Bernoulli continued fraction
Author:
J. S. Frame
Journal:
Math. Comp. 33 (1979), 815-826
MSC:
Primary 65F30
DOI:
https://doi.org/10.1090/S0025-5718-1979-0521297-0
MathSciNet review:
521297
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Abstract | References | Similar Articles | Additional Information
Abstract: The Hankel power sum matrix
(where V is the
Vandermonde matrix) has (i, j)-entry
, where
. In solving a statistical problem on curve fitting it was required to determine
so that for
all eigenvalues of
would be less than 1. It is proved, after calcu lating
by first factoring W into easily invertible factors, that
suffices. As by-products of the proof, close approximations are given for the Hilbert determinant, and a convergent continued fraction with mth partial denominator
is found for the divergent Bernoulli number series
.
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1979-0521297-0
Article copyright:
© Copyright 1979
American Mathematical Society