seemps.analysis.expansion.PowerExpansion

class seemps.analysis.expansion.PowerExpansion

Bases: PolynomialExpansion

Polynomial expansion in the monomial basis {1, x, x^2, …}, coresponding to a standard power or Taylor series.

The recurrence relation is trivial, P_{k+1}(x) = x · P_k(x), and the basis is not orthogonal with respect to any inner product (orthogonality_domain is None).

When evaluated using the Clenshaw recursion, this expansion reduces to Horner’s method, providing a numerically stable and efficient evaluation of polynomial functions in tensor-network form.

recurrence_coefficients(k: int) → tuple[float, float, float]

Return the three-term coefficients (α_k, β_k, γ_k) for the recursion P_{k+1}(x) = (α_k x + β_k) P_k(x) - γ_k P_{k-1}(x).