PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 56(70), pp. 4153 (1994) 

Sur l'itere de $\sin x$Farid Bensherif et Guy RobinDépartement d'algèbre, U.S.T.H.B., Alger, Algérie. and LACO, Laboratoire d'arithmétique, de calcul formel $ & $ d'optimisation, URA 1586, Faculté des Sciences, 123, avenue Albert Thomas, 87060 Limoges, FranceAbstract: We show that the asymptotic expansion of the sequence $x_n = \sin x_{n1}$ with $x_0 = x(x\in]0,\pi[)$, as $n$ goes to $+\infty$, uses a family of polynomials (with rational coefficients) which are linked by relations of recurrency. The study applies to a large class of sequences. We finish by a sharp study of the sinus function. Classification (MSC2000): 10H25; 41A10 Full text of the article:
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