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The Hankel transform and some of its properties.

John W. Layman

Open publisher page 201 citations

Abstract

The Hankel transform of an integer sequence is defined and some of its properties discussed. It is shown that the Hankel transform of a sequence S is the same as the Hankel transform of the Binomial or Invert transform of S. If H is the Hankel matrix of a sequence and H=LU is the LU decomposition of H, the behavior of the first super-diagonal of U under the Binomial or Invert transform is also studied. This leads to a simple classification scheme for certain integer sequences. 1.

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What this paper is about

The Hankel transform of an integer sequence is defined and some of its properties discussed. It is shown that the Hankel transform of a sequence S is the same as the Hankel transform of the Binomial or Invert transform of S. If H is the Hankel matrix of a sequence and H=LU is the LU decomposition of H, the behavior of the first super-diagonal of U under the Binomial or Invert transform is also studied. This leads to a simple classification scheme for certain integer sequences. 1.

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OpenAlex reports 201 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The Hankel transform of an integer sequence is defined and some of its properties discussed. It is shown that the Hankel transform of a sequence S is the same as the Hankel transform of the Binomial or Invert transform of S. If H is the Hankel matrix of a sequence and H=LU is the LU decomposition of H, the behavior of the first super-diagonal of U under the Binomial or Invert transform is also studied. This leads to a simple classification scheme for certain integer sequences. 1.

Key concepts: Hankel matrix, Hankel transform, Mathematics, Sequence (biology), Diagonal, Integer (computer science), Combinatorics, Mathematical analysis

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