Antisymmetric Orthogonal Polynomials: Recurrence Relation
Recall from Recurrence Relation Page that the Antisymmetric OP can be generated by a three-term recurrence relation:
where the bk, ck, and dk^2 are coefficients which are generated simultaneously in the recurrence relation.
On the left we plots the coefficients dk2, bk, and ck versus the degree k. Note that the dk2 exhibit exponential growth, while the bk and ck show exponential decay. Also note that the values of the coefficients are taken in log scale.
On the right we plot the coeffients broken into two categories: even degree k and odd degree k. Even k is plotted in red and odd k is plotted in blue.
Note, click on any plot to enlarge it.
