Question

A significant outcome from Hermite's equation are the Hermite Polynomials Hn(x). They are the nth-order polynomial solution toHermite's equation(v or v,) multiplied by an appropriate constant cn such that the coefficient of x" is 21. (a) Find the first three even Hermite Polynomials. That is, to find Ho(x) find a constant co to multiply with y1 when α-0 such that the coefficient in front of xo is 20. To find H2 (x) find a constant c2 to multiply with y1 when α-2 such that the coefficient in front of x2 is 22. To find H, (x) find a constant C4 to multiply with y1 when α 4 such that the coefficient in front of x* is 2 (b) Find the first three odd Hermite Polynomials. That is, to find H1(x) find a constant c,1 to multiply with y2 when α-1 such that the coefficient in front of x 1 is 21 . TO find H3 (x) find a constant C3 to multiply with ½ when α-3 such that the coefficient in front of x3 is 23. To find He(x) find a constant cs to multiply with y, when α = 5 such that the coefficient in front of x is 2

Answer 1

tue have 2t t2 21 t-42 o! 2. 5) 3! 2 21 20 5

o( Y evan sor ond 20