Pith. Sign in

RECORD

DEK-Type orthogonal polynomials and a modification of the Christoffel formula

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Rachel Bailey, Maxim Derevyagin

Mathematical Physics · Submitted 6 Oct 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We dissect the DEK polynomials using the discrete Darboux transformations and unravel a characterization bypassing the differential equation that defines the DEK polynomials.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2110.03038 (version 4)
Pith ID2R5HI2KL, Pith's permanent record of this paper and its review
CitationMaxim Derevyagin, Rachel Bailey. "DEK-Type orthogonal polynomials and a modification of the Christoffel formula." arXiv:2110.03038 (2021). https://pith.science/paper/2R5HI2KL
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,739 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.76 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

In this note we revisit one of the first known examples of exceptional orthogonal polynomials that was introduced by Dubov, Eleonskii, and Kulagin in relation to nonharmonic oscillators with equidistant spectra. We dissect the DEK polynomials using the discrete Darboux transformations and unravel a characterization bypassing the differential equation that defines the DEK polynomials. This characterization also leads to a family of general orthogonal polynomials with missing degrees and this approach manifests its relation to biorthogonal polynomials introduced by Iserles and N{\o}rsett, which are applicable to a whole range of problems in computational and applied analysis. We also obtain a modification of the Christoffel formula for this family since its classical form cannot be applied in this case.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this note we revisit one of the first known examples of exceptional orthogonal polynomials that was introduced by Dubov, Eleonskii, and Kulagin in relation to nonharmonic oscillators with equidistant spectra. background 0.96 0.30 0.06 asserted 0.99
s1 We dissect the DEK polynomials using the discrete Darboux transformations and unravel a characterization bypassing the differential equation that defines the DEK polynomials. contribution 0.70 0.95 0.27 asserted 1.00
s2 This characterization also leads to a family of general orthogonal polynomials with missing degrees and this approach manifests its relation to biorthogonal polynomials introduced by Iserles and N{\o}rsett, which are applicable to a whole range of problems in computational and applied analysis. result 0.51 0.85 0.32 asserted 1.00
s3 We also obtain a modification of the Christoffel formula for this family since its classical form cannot be applied in this case. result 0.63 0.95 0.27 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this note we revisit one of the first known examples of exceptional orthogonal polynomials that was introduced by Dubov, Eleonskii, and Kulagin in relation to nonharmonic oscillators with equidistant spectra. We dissect the DEK polynomials using the discrete Darboux transformations and unravel a characterization bypassing the differential equation that defines the DEK polynomials. This characterization also leads to a family of general orthogonal polynomials with missing degrees and this approach manifests its relation to biorthogonal polynomials introduced by Iserles and N{\o}rsett, which are applicable to a whole range of problems in computational and applied analysis. We also obtain a modification of the Christoffel formula for this family since its classical form cannot be applied in this case.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.