General Orthogonal Polynomial Series

The base orthax module provides a number of functions useful for dealing with general orthogonal polynomial series, based around the idea of the three term recurrence relation.

Arithmetic

orthadd(c1, c2, rec)	Add one orthogonal series to another.
orthsub(c1, c2, rec)	Subtract one orthogonal series from another.
orthmulx(c, rec[, mode])	Multiply an orthogonal series by x.
orthmul(c1, c2, rec[, mode])	Multiply one orthogonal series by another.
orthpow(c, pow, rec[, maxpower])	Raise an orthogonal series to a power.
orthval(x, c, rec[, tensor])	Evaluate an orthogonal series.
orthval2d(x, y, c, rec)	Evaluate a 2-D orthogonal series at points (x, y).
orthval3d(x, y, z, c, rec)	Evaluate a 3-D orthogonal series at points (x, y, z).
orthgrid2d(x, y, c, rec)	Evaluate a 2-D orthogonal series on the Cartesian product of x and y.
orthgrid3d(x, y, z, c, rec)	Evaluate a 3-D orthogonal series on the Cartesian product of x, y, and z.

Calculus

orthder(c, rec[, m, scl, axis])	Differentiate an orthogonal series.
orthint(c, rec[, m, k, lbnd, scl, axis])	Integrate an orthogonal series.

Misc Functions

orthfromroots(roots, rec)	Generate an orthogonal series with given roots.
orthroots(c, rec)	Compute the roots of an orthogonal series.
orthvander(x, deg, rec)	Pseudo-Vandermonde matrix of given degree.
orthvander2d(x, y, deg, rec)	Pseudo-Vandermonde matrix of given degrees.
orthvander3d(x, y, z, deg, rec)	Pseudo-Vandermonde matrix of given degrees.
orthgauss(deg, rec[, x0, x1])	Compute Gaussian quadrature nodes and weights for given orthogonal polynomials.
orthweight(x, rec)	Weight function of orthogonal polynomials.
orthnorm(n, rec)	Norm of nth orthogonal polynomial.
orthcompanion(c, rec)	Return the companion matrix of c.
orthfit(x, y, deg, rec[, rcond, full, w])	Least squares fit of orthogonal series to data.
orthtrim(c[, tol])	Remove "small" "trailing" coefficients from a polynomial.
orthline(off, scl, rec)	Orthogonal series whose graph is a straight line.
orth2poly(c, rec)	Convert an orthogonal series to a polynomial in standard basis.
poly2orth(pol, rec)	Convert a polynomial to an orthogonal series.