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(a) Hermite polynomials can be obtained through the Rodrigues formula H₂(x) = (−1)ªe²² where H₂= dHn/dx. The function n d d.x n Determine H3(x) using this method. (b) Hermite polynomials satisfy the differential equation H"(z)−2rH,(z)+2nHn(r)=0, h(x) = x² e 2² 1 2 is a Hermite polynomial. Using the differential equation, determine its value of n?

(a) Hermite polynomials can be obtained through the Rodrigues formula H₂(x) = (−1)ªe²² where H₂= dHn/dx. The function n d d.x n Determine H3(x) using this method. (b) Hermite polynomials satisfy the differential equation H"(z)−2rH,(z)+2nHn(r)=0, h(x) = x² e 2² 1 2 is a Hermite polynomial. Using the differential equation, determine its value of n?

Advanced Engineering Mathematics
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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(a) Hermite polynomials can be obtained through the Rodrigues formula H₂(x) = (−1)ªe²² where H₂= dHn/dx. The function n d d.x n Determine H3(x) using this method. (b) Hermite polynomials satisfy the differential equation H"(z)−2rH,(z)+2nHn(r)=0, h(x) = x² e 2² 1 2 is a Hermite polynomial. Using the differential equation, determine its value of n?
Transcribed Image Text:(a) Hermite polynomials can be obtained through the Rodrigues formula H₂(x) = (−1)ªe²² where H₂= dHn/dx. The function n d d.x n Determine H3(x) using this method. (b) Hermite polynomials satisfy the differential equation H"(z)−2rH,(z)+2nHn(r)=0, h(x) = x² e 2² 1 2 is a Hermite polynomial. Using the differential equation, determine its value of n?
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