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Positivity properties of some special matrices
Published in Elsevier Inc.
Volume: 596
Pages: 203 - 215
It is shown that for positive real numbers 0<λ1<…<λn, [Formula presented], where β(⋅,⋅) denotes the beta function, is infinitely divisible and totally positive. For [Formula presented], the Cholesky decomposition and successive elementary bidiagonal decomposition are computed. Let w(n) be the nth Bell number. It is proved that [w(i+j)] is a totally positive matrix but is infinitely divisible only upto order 4. It is also shown that the symmetrized Stirling matrices are totally positive. © 2020 Elsevier Inc.
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