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Some methods for the evaluation of complicated Feynman integrals

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A. V. Kotikov

High Energy Physics - Phenomenology · Submitted 28 Dec 2001

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

The authors' main claim We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most complicated part of O(1/N^3) contributions to critical exponents of \phi^4-theory.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-ph/0112347 (version 1)
Pith IDABAMO26K, Pith's permanent record of this paper and its review
CitationA. V. Kotikov. "Some methods for the evaluation of complicated Feynman integrals." arXiv:hep-ph/0112347 (2001). https://pith.science/paper/ABAMO26K
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,908 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most complicated part of O(1/N^3) contributions to critical exponents of \phi^4-theory. An illustration of the results obtained with help of above methods is considered.

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 We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. contribution 0.52 0.63 0.27 asserted 0.95
s1 We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most complicated part of O(1/N^3) contributions to critical exponents of \phi^4-theory. result 0.78 0.92 0.41 asserted 1.00
s2 An illustration of the results obtained with help of above methods is considered. contribution 0.73 0.63 0.07 asserted 0.73

What kind of paper the classifier reports this is: method or tool 0.73 · evidence from proof or derivation 0.81.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most complicated part of O(1/N^3) contributions to critical exponents of \phi^4-theory. An illustration of the results obtained with help of above methods is considered.

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References
How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper
  • Nowadays we are not at the point to have the method for evaluating any Feynman integral, but certainly we dispose of several tools [ref] to attack successfully many problems in perturbation theory, and usually a combination of them is necessary for the achievement of the final answer.

    Feynman Diagrams and Differential Equations · Introduction · 0.86

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