Cornell University Math REU

• Results
• Antisymmetric OP
• Symmetric OP
• Orthonormal OP
• Comparison
  1. Compare Graphs
  2. Compare Reccurence
  3. Compare Edge Plots
  4. Compare Zero Plots
  5. Compare Dynamics
• Home

Compare Antisymmetric and Symmetric OP: Recurrence Relations

Recall from Recurrence Relation Page that both the Antisymmetric and Symmetric OP can be generated by a three-term recurrence relation:

p_k+1(x) = f_k+1(x) − b_k p_k(x) − c_k p_k-1(x)

where the b_k, c_k, and d_k^2 are coefficients which are generated simultaneously in the recurrence relation. And similarly for the s_k.

First we plots the coefficients d_k², b_k, and c_k versus the degree k. The Antisymmetric OP are shown on the left, and the Symmetric OP on the right. Note that both OP have coefficients with similar behavior.

Next 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. The Antisymmetric OP are shown on the left, and the Symmetric OP on the right.