What is a vector Hankel determinant
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چکیده
منابع مشابه
A Catalan-Hankel Determinant Evaluation
Let Ck = ( 2k k ) /(k+1) denote the k-th Catalan number and put ak(x) = Ck+Ck−1x+· · ·+C0x . Define the (n+1)×(n+1) Hankel determinant by setting Hn(x) = det[ai+j(x)]0≤i,j≤n. Even though Hn(x) does not admit a product form evaluation for arbitrary x, the recently introduced technique of γ-operators is applicable. We illustrate this technique by evaluating this Hankel determinant as Hn(x) = n ∑
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The purpose of this note is two-fold. First we present evaluations of Hankel determinants of sequences of combinatorial interest related to partitions and permutations. Many such computations have been carried out by Radoux in his sequence of papers [2]–[5]. His proof methods include using a functional identity due to Sylvester and factoring the Hankel matrix. Second, unlike Radoux, we instead ...
متن کاملHankel Determinant Solution for Elliptic Sequence
We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the Hankel determinants. PACS numbers: 02.30.Ik, 02.30.Gp, 02.30.Lt
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)10091-x