Question

ou Problem 10.4.3. Show that the first four Hermite polynomials are im Ho = Hi = 2y (10.4.35) (10.4.36)

Answer 1

I co know that the Hermite polynomial of ordern is Hon (g) = 5 Goro ni ! p20 min-2018 where 1/2 it n is even nel if nis odd 1-270); (27;"-27 2 0- 20 rod Hogs – Š 105 106 107 Cayman 7 (2) , 4. 1-200 H ($D = ,(2 = 1.(29)' 327 H, (v) : eva (1) 12- 20 z (23-24. 1. 162492 - 2-2 (1-27 2 p! 8-2n)!. Hz(t)= È Cym. Spy ( 2 (24)3 – 6.(24) = 843 – 12y = -12 (y – žys)

orthogonality prool: The generating function gwes o & Honeys.sim e2sys multiplying we get Ancg). Hmly me mzo nimi 2 e 2ty t tasy-s? multiplying both side by eye sehen integrate wart one from a too, we get Il exindys. Homoge diye : = 5e87344-)=67€) dy --Sestryltos) -easiektas? Cuplay zey J * 2+1}=(tending telepon 9 a clearly whene men eguating coeffierent of tsh in both sides do oro me get Se Hage Homes dy zo - when man, equating the coefficent of t so from both side of ③ nina s Et Fitney Jaya 2 song a to z STEHT aya uzani to twy

combinding @ and (w me hal et do in (y). Him (1) dy z Son (52":ni)