# Student t orthogonal polynomials

1. Jul 20, 2011

### 64jnk

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. Jul 20, 2011

### kdbnlin78

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!)

3. Jul 24, 2011

### 64jnk

That's done the trick. Thank you.