orthax.recurrence.TabulatedRecurrenceRelation

class orthax.recurrence.TabulatedRecurrenceRelation(weight: Callable, domain: tuple, ak: Array, bk: Array, gk: Array, mk: Array | None = None)Source

Recurrence relation from tabulated values.

Parameters:

• weight (callable) – Weight function.

• domain (tuple) – Lower and upper bounds for inner product defining orthogonality.

• a (jax.Array) – Coefficients of the monic three term recurrence relation.

• b (jax.Array) – Coefficients of the monic three term recurrence relation.

• g (jax.Array) – g[k] is the weighted norm of the kth monic orthogonal polynomial.

• m (jax.Array) – m[k] is the coefficient of x**k in the kth orthogonal polynomial in the desired normalization. Default is 1 (monic form). For normalized form, set m = 1/g

__init__(weight: Callable, domain: tuple, ak: Array, bk: Array, gk: Array, mk: Array | None = None)Source

Methods

__init__(weight, domain, ak, bk, gk[, mk])
a(k)	a coefficients of the monic three term recurrence relation.
b(k)	b coefficients of the monic three term recurrence relation.
g(k)	Weighted norm of the kth monic orthogonal polynomial.
m(k)	Coefficient of x**k in the kth polynomial in the desired normalization.
weight(x)	Weight function defining inner product.

Attributes

domain

Lower and upper bounds for inner product defining orthogonality.