Note on N‐dimensional hermite polynomials

I t is well known that a complete set of orthonormal polynomials in N variables can be obtained by using products of such polynomials in a single variahle. Such a procedure lacks symmetry, and there is sometimes an advantage to be gained by expressing the polynomials in tensor invariant notation. The -\--vector z,(i = 1, 2, . . . , X ) is denoted by x. The second order tensor (dyad) X , X , is denoted by x'. Similarly, xn is used for the n-th order tensor x,,xi2 x,, . For the scalar product I t is convenient to introduce a special notation.