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Titolo:
An inequality involving the generalized hypergeometric function and the arc length of an ellipse
Autore:
Barnard, RW; Pearce, K; Richards, KC;
Indirizzi:
Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA Texas Tech Univ Lubbock TX USA 79409 t Math & Stat, Lubbock, TX 79409 USA Southwestern Univ, Dept Math, Georgetown, TX 78626 USA Southwestern Univ Georgetown TX USA 78626 Math, Georgetown, TX 78626 USA
Titolo Testata:
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
fascicolo: 3, volume: 31, anno: 2000,
pagine: 693 - 699
SICI:
0036-1410(20000306)31:3<693:AIITGH>2.0.ZU;2-G
Fonte:
ISI
Lingua:
ENG
Keywords:
hypergeometric; approximations; elliptical arc length;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
13
Recensione:
Indirizzi per estratti:
Indirizzo: Barnard, RW Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA TexasTech Univ Lubbock TX USA 79409 t, Lubbock, TX 79409 USA
Citazione:
R.W. Barnard et al., "An inequality involving the generalized hypergeometric function and the arc length of an ellipse", SIAM J MATH, 31(3), 2000, pp. 693-699

Abstract

In this paper we verify a conjecture of M. Vuorinen that the Muir approximation is a lower approximation to the arc length of an ellipse. Vuorinen conjectured that f (x) = F-2(1) (1/2, -1/2; 1; x) [(1 + (1-x)(3/4))/2](2/3) is positive for x is an element of (0, 1). The authors prove a much strongerresult which says that the Maclaurin coefficients of f are nonnegative. Asa key lemma, we show that F-3(2) (-n, a, b; 1+ a + b, 1+ epsilon-n; 1) > 0when 0 < ab/(1 + a + b) < epsilon < 1 for all positive integers n.

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Documento generato il 05/12/20 alle ore 01:55:42