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On the integral of products of higher-order Bernoulli and Euler polynomials

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M. Cihat Dagli, Mümün Can

Number Theory · Submitted 29 Sep 2016

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

The authors' main claim In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials.

how it is stated · asserted 1.00 read the record →

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arXiv ID1609.09336 (version 1)
Pith IDXZEOUPEV, Pith's permanent record of this paper and its review
CitationM. Cihat Dagli, M\"um\"un Can. "On the integral of products of higher-order Bernoulli and Euler polynomials." arXiv:1609.09336 (2016). https://pith.science/paper/XZEOUPEV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,508 input tokens.

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 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials. Moreover, we establish the connection between the results and the generalized Dedekind sums and Hardy--Berndt sums. Finally, the Laplace transform of Euler polynomials is given.

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 derive a formula on the integral of products of the higher-order Euler polynomials. contribution 0.90 0.97 0.63 asserted 1.00
s1 By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials. result 0.67 0.93 0.13 asserted 1.00
s2 Moreover, we establish the connection between the results and the generalized Dedekind sums and Hardy--Berndt sums. result 0.54 0.94 0.20 asserted 1.00
s3 Finally, the Laplace transform of Euler polynomials is given. result 0.72 0.94 0.11 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 derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials. Moreover, we establish the connection between the results and the generalized Dedekind sums and Hardy--Berndt sums. Finally, the Laplace transform of Euler polynomials is given.

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