ABSTRACT
DEFINITION 6 . 7 . 1 . T h e funct ion Hv[x) = (-l)"ex2(e-x2)("\ v = 0 , 1 . . . ( 6 . 7 . 1 )
is cal led the Hermi te po lynomia l .
C a r r y i n g out differentiation i n ( 6 . 7 . 1 ) we find HQ(X) = 1, Hi(x) = 2x, H2(x) = 4 x 2 — 2 , . . . A simple verif icat ion shows that
R
Set := (2kk\y/Z)~ie-'*-Hk(x).
