(c) If you differentiate an nth-order polynomial, you get a polynomial of order (n-1). For the hermite polynomials, in fact, dHn ἀξ = 2nHn-1(E) Check this, by differentiating H5 and H6. (d) H₂() is the nth z-derivative, at z = 0, of the generating function exp(-2₂² +2z§); or, to put it another way, it is the coefficient of z"/n! in the Taylor series expansion for this function: e¯²³²+2=² = Σ n=0 Use this to obtain H₁, H₂, and H3. n! (3) H₂(8) (4)
(c) If you differentiate an nth-order polynomial, you get a polynomial of order (n-1). For the hermite polynomials, in fact, dHn ἀξ = 2nHn-1(E) Check this, by differentiating H5 and H6. (d) H₂() is the nth z-derivative, at z = 0, of the generating function exp(-2₂² +2z§); or, to put it another way, it is the coefficient of z"/n! in the Taylor series expansion for this function: e¯²³²+2=² = Σ n=0 Use this to obtain H₁, H₂, and H3. n! (3) H₂(8) (4)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 66E
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