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A Generalization of Landen's Quadratic Transformation Formulas for Jacobi Elliptic Functions

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Avinash Khare, Uday Sukhatme

Mathematical Physics · Submitted 30 Apr 2002

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

The authors' main claim We obtain and discuss significant generalizations of the celebrated Landen formulas.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath-ph/0204054 (version 1)
Pith IDCDQKCHDQ, Pith's permanent record of this paper and its review
CitationAvinash Khare, Uday Sukhatme. "A Generalization of Landen's Quadratic Transformation Formulas for Jacobi Elliptic Functions." arXiv:math-ph/0204054 (2002). https://pith.science/paper/CDQKCHDQ
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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, 2,926 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.61 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transformation of variables in elliptic integrals. We obtain and discuss significant generalizations of the celebrated Landen formulas. Our approach is based on some recently obtained periodic solutions of physically interesting nonlinear differential equations and numerous remarkable new cyclic identities involving Jacobi elliptic functions.

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 Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transformation of variables in elliptic integrals. background 1.00 0.03 0.03 asserted 1.00
s1 We obtain and discuss significant generalizations of the celebrated Landen formulas. contribution 0.96 0.96 0.81 asserted 1.00
s2 Our approach is based on some recently obtained periodic solutions of physically interesting nonlinear differential equations and numerous remarkable new cyclic identities involving Jacobi elliptic functions. method 0.99 0.84 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • P abstract
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  • 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

Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transformation of variables in elliptic integrals. We obtain and discuss significant generalizations of the celebrated Landen formulas. Our approach is based on some recently obtained periodic solutions of physically interesting nonlinear differential equations and numerous remarkable new cyclic identities involving Jacobi elliptic functions.

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