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A set of orthogonal polynomials, dual to alternative q-Charlier polynomials

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N. M. Atakishiyev, A. U. Klimyk

Classical Analysis and ODEs · Submitted 16 Dec 2003

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

The authors' main claim The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials.

how it is stated · asserted 0.97 read the record →

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arXiv IDmath/0312312 (version 1)
Pith IDBXUZXQIA, Pith's permanent record of this paper and its review
CitationA. U. Klimyk, N. M. Atakishiyev. "A set of orthogonal polynomials, dual to alternative q-Charlier polynomials." arXiv:math/0312312 (2003). https://pith.science/paper/BXUZXQIA
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,933 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a three-term recurrence relation for these dual polynomials are explicitly obtained. The completeness property of dual alternative q-Charlier polynomials is also established.

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 The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. contribution 1.00 0.91 0.47 asserted 0.97
s1 A discrete orthogonality relation and a three-term recurrence relation for these dual polynomials are explicitly obtained. result 0.95 0.95 0.18 asserted 1.00
s2 The completeness property of dual alternative q-Charlier polynomials is also established. result 0.94 0.91 0.18 asserted 1.00

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

What was examined, and what was not

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  • C citations
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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

The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a three-term recurrence relation for these dual polynomials are explicitly obtained. The completeness property of dual alternative q-Charlier polynomials is also established.

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