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: 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 *m*th partial denominator is found for the divergent Bernoulli number series .

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0521297-0

Article copyright:
© Copyright 1979
American Mathematical Society