Two-point Taylor Expansions of Analytic Functions

(2) CWI; Amsterdam); Jose L. Lopez (1); Nico M. Temme (2) ((1) Universidad Publica de Navarra; Pamplona

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Two-point Taylor Expansions of Analytic Functions

Jose L. Lopez (1), Nico M. Temme (2) ((1) Universidad Publica de Navarra, Pamplona, (2) CWI, Amsterdam)

Classical Analysis and ODEs · Submitted 7 May 2002

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

The authors' main claim Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated.

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arXiv IDmath/0205064 (version 1)

Pith IDB2KZM6O3, Pith's permanent record of this paper and its review

Citation(2) CWI, Amsterdam), Jose L. Lopez (1), Nico M. Temme (2) ((1) Universidad Publica de Navarra, Pamplona. "Two-point Taylor Expansions of Analytic Functions." arXiv:math/0205064 (2002). https://pith.science/paper/B2KZM6O3

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What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.02.

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Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in two points.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Taylor expansions of analytic functions are considered with respect to two points.	background 0.59	0.53	0.09	asserted 0.96
s1	Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated.	contribution 0.71	0.87	0.19	asserted 1.00
s2	It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals.	contribution 0.66	0.73	0.17	asserted 0.95
s3	The method is also used for obtaining Laurent expansions in two points.	contribution 0.78	0.83	0.11	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.71 · evidence from proof or derivation 1.00.

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Original abstract

Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in two points.

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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

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The UAE procedure is expressing $F_E(e,t)$ in terms of the following Laurent series [ref] , [equation] Substituting it it into the integral ([ref]), one would obtain the integrals that take the form of [equation] With the help of the expansion, [equation] where $h_0:=(4ζ/Δ_e^2)^1/4$.

Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms · $(p,a,0)$ · 0.98

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