The Evaluate routine evaluates finite orthogonal series of one or more variables using a generalization of the Horner scheme.

The generalized Horner scheme accepts only finite series, that is, polynomials, but S can be a infinite series if the truncation option is used. This option has the form trunc=[t1,...,tn], where  is the dimension of the series S and t1,...,tn are non-negative integers. The Evaluate(S, arguments, trunc=[t1,..., tn]) calling sequence is equivalent to Evaluate(Truncate(S, [t1,..., tn]), arguments). For  equal to 1 the list format is not required. You can replace trunc=[t1] with trunc=t1.

The Evaluate(S) calling sequence returns the series S in the canonical basis.

The Evaluate(S, x=v) calling sequence evaluates the series S after substituting the value v for the variable x. More generally, the Evaluate(S, [x1=v1,..., xk=vk]) calling sequence evaluates the series S after substituting each value vi for the corresponding variable xi. If x or xi is not a variable of S, the substitution is ignored. If there exists i and j such that xi=xj in the substitution list, only the first substitution is performed. If the number of substitutions is less than the dimension of S, the result of the Evaluate function is a new orthogonal series with () variables. Otherwise, the result is an algebraic expression.

The Evaluate(S, v) calling sequence evaluates the univariate series S after substituting the value v for the variable. The Evaluate(S, [v1,..., vn]) calling sequence evaluates the series of dimension n S after substituting each vi for the corresponding ith variable. If n is not the dimension of S, an error is returned.

Error, (in OrthogonalSeries:-Evaluate) infinite number of terms