Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Student t orthogonal polynomials

  1. Jul 20, 2011 #1
    I've just read a paper that references the use of student-t orthogonal polynomials. I understand how the Gauss-Hermite polynomials are derived, however applying the same process to the weight function (1 + t^2/v)^-(v+1)/2 I can't quite get an answer that looks anything like a polynomial.

    Would anyone be able to provide me with the student-t polynomials, which I can check my derivation against?

    Thank you.
     
  2. jcsd
  3. Jul 20, 2011 #2
    As far as I can remember you should end up with the prthogonal polynomials taking the form

    /phi_{m}(t) = A_{m}/[1+/frac{t^{2}}{v}/]/frac{d^{m}}{dt^{m}}/[/frac{1}{1+/frac(t^{2}}{v}}^{/frac{v-1}{2}-m}/]

    Then,

    /int_{- /infty}^{+ /infty} /frac{1}{1+/frac{t^{2}}{v}}^{frac{v+1}{2}}/phi_{m}(t}/phi_{n}(t) dt=0

    (hope all teX commands are in the right place!)
     
  4. Jul 24, 2011 #3
    That's done the trick. Thank you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook