Polynômes orthogonaux de Tchebychev et ses applications

Abstract

𝐿𝑛 𝑥 𝑥𝑘 𝑤 𝑥 = 0, 𝑘 = 0,1,2, … , 𝑛 − 1 … 𝑏 𝑎 تحقق علاقات التعامد 𝑤 𝑥 أي 𝐿𝑛 𝑧 أكثز من نقطة 𝑎 , 𝑏 شكل كث زٍات حدود تش بٍ شٍاف على القطعة 𝐿𝑛 ل كٍن التال ةٍ: 𝑎 , 𝑏 = −1 , 1 , 𝑤 𝑥 = لتكن 1 1−𝑥2 ف تعز فٌ كث زٍ حدود تش بٍ شٍاف ، قمنا ف مذكزتنا هذه بدراسة خصائص كث زٍات حدود تش بٍ شٍاف.Let 𝜇 be a finite positive measure defined on the Borelian 𝜎 −algebra of C, 𝜇 is absolutely continuous with respect to the Lebesgue measure𝑑 𝑥 𝑜𝑛 𝑎 , 𝑏 . Let us consider 𝐿𝑛 𝑧 𝑛∈𝑁 , the system of monic orthogonal polynomial with respect to 𝑤 𝑥 𝑑𝑥. Such that: We choose 𝑎 , 𝑏 = −1 , 1 , 𝑤 𝑥 = 1 1−𝑥2 which called Tchebychev orthogonal polynomials. We study algebraic and asymptotic properties of the Tchebychev orthogonal polynomials.