16. Concerning the polynomial p(x) = ao+a₁x + +a,x", prove the following result. Fora given x, we set (an, Bn Yn) = (an , 0, 0) and define inductively(a₁, B₁, v₁) = (a; + xα₁ + 1, α₁ +1 +xBj+1, Bj+1 + xy j +1)for j =n-1, n-2,...,0. Then p(x) = ao, p'(x) = Bo, and p"(x) = 270.

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Answered: Concerning the polynomial p(x) = ao+a₁x…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concerning the polynomial p(x) = ao+a₁x + +anx", prove the following result. For a given x, we set (an, Pn, Yn) = (an, 0, 0) and define inductively (aj, B₁, y) = (a + xαj+1, α;+1+xBj+1, B₁+1 + xyj+1) for j=n-1, n-2,...,0. Then p(x) = ao, p'(x) = Bo, and p"(x) = 270.