Question 4: Let F(x, t) = (1 − 2xt + t²)-¹. Show that F(x,t) = Σ Sn(x)t", where n=0 [n/2] (n+1)!(1-x²) mxn-2m Sn(x) = Σ m=0 (2m+1)!(n-2m)! The polynomial S, is the nth degree Tchebycheff polynomial of the second kind. Question 5: The Hermite polynomials H₁ are generated by the function F(x,t) = exp(2xt-t²): F(x,t) = Hn(x) th n=0 n! Show that (a) Fx(x, t)=2tF(x, t) (b) F(x, t)=2(x − t) F(x, t).

Question 4: Let F(x, t) = (1 − 2xt + t²)-¹. Show that F(x,t) = Σ Sn(x)t", where n=0 [n/2] (n+1)!(1-x²) mxn-2m Sn(x) = Σ m=0 (2m+1)!(n-2m)! The polynomial S, is the nth degree Tchebycheff polynomial of the second kind. Question 5: The Hermite polynomials H₁ are generated by the function F(x,t) = exp(2xt-t²): F(x,t) = Hn(x) th n=0 n! Show that (a) Fx(x, t)=2tF(x, t) (b) F(x, t)=2(x − t) F(x, t).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 3E

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