Hankel determinant

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1: 3.9 Acceleration of Convergence

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3.9.9 $$t_{n,2k}=\frac{H_{k+1}(s_n)}{H_k({\mathrm{\Delta }}^2{s}_n)},$$ $n=0,1,2,\mathrm{\dots }$,

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Symbols:

$s_n$: sequence, $t_n$: sequence and $H_m(u)$: Hankel determinant

Referenced by:

§3.9(iv)

Permalink:

http://dlmf.nist.gov/3.9.E9

Encodings:

pMML, png, TeX

See also:

Annotations for §3.9(iv), §3.9 and Ch.3

►where $H_m$ is the Hankel determinant ►

3.9.10

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Defines:

$H_m(u)$: Hankel determinant (locally)

Symbols:

$det$: determinant

Permalink:

http://dlmf.nist.gov/3.9.E10

Encodings:

pMML, png, TeX

See also:

Annotations for §3.9(iv), §3.9 and Ch.3

►The ratio of the Hankel determinants in (3.9.9) can be computed recursively by Wynn’s epsilon algorithm: …

2: 24.14 Sums

… ►These identities can be regarded as higher-order recurrences. Let $det[a_{r+s}]$ denote a Hankel (or persymmetric) determinant, that is, an $(n+1)\times (n+1)$ determinant with element $a_{r+s}$ in row $r$ and column $s$ for $r,s=0,1,\mathrm{\dots },n$. …

3: 18.2 General Orthogonal Polynomials

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§18.2(ix) Moments

… ►The Hankel determinant ${\mathrm{\Delta }}_n$ of order $n$ is defined by ${\mathrm{\Delta }}_0=1$ and …It is to be noted that, although formally correct, the results of (18.2.30) are of little utility for numerical work, as Hankel determinants are notoriously ill-conditioned. …