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The values of the high order Bernoulli polynomials at integers and the r-Stirling numbers

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Miloud Mihoubi, Meriem Tiachachat

Number Theory · Submitted 23 Jan 2014

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

The authors' main claim In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers.

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arXiv ID1401.5958 (version 1)
Pith ID4ZBPUX4L, Pith's permanent record of this paper and its review
CitationMeriem Tiachachat, Miloud Mihoubi. "The values of the high order Bernoulli polynomials at integers and the r-Stirling numbers." arXiv:1401.5958 (2014). https://pith.science/paper/4ZBPUX4L
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,274 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the r-Stirling numbers and binomial coefficients.

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 paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. contribution 0.96 0.95 0.81 asserted 1.00
s1 We give also some identities linked the r-Stirling numbers and binomial coefficients. result 0.58 0.94 0.10 asserted 1.00

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

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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

In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the r-Stirling numbers and binomial coefficients.

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