orthax.recurrence.AbstractRecurrenceRelation

class orthax.recurrence.AbstractRecurrenceRelation(_domain: tuple[float, float])Source

Base class for three term recurrence relations.

Subclasses should declare attributes and _domain and implement methods weight, a, b, g, m

__init__(_domain: tuple[float, float]) → None

Methods

__init__(_domain)
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.