Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

Denote by $h_n$ the $n$-th Hermite function. $$ h_n(x) = \frac{(-1)^n }{\sqrt{2^n n! \sqrt{\pi}}} \mathrm{e}^{\frac{x^2}{2}} \frac{\mathrm{d}^n}{\mathrm{d} x^n} \mathrm{e}^{-x^2} $$

I am trying to find the 40th, 41st and 42nd terms in Gram-Schmidt process with Hermite functions $h_n$ on $[-1, 1]$.

I've used the usual procedure for Gram-Schmidt process, but I've been able to calulate only the first 6 terms and then my computer got stuck.

Is there some way to calculate them?

share|improve this question
    
Is this question related to Mathematica (TM)? Can you post your Mathematica code? –  belisarius Jul 2 '13 at 17:24
    
Have you seen this? functions.wolfram.com/HypergeometricFunctions/HermiteHGeneral/… –  bill s Jul 2 '13 at 17:30
    
Related (duplicate?): mathematica.stackexchange.com/q/22040/5 –  rm -rf Jul 2 '13 at 17:32
    
@ bill s: as I understand, its Hermit polynomial-not function... –  Mack Jul 2 '13 at 17:40
4  
To the closers: I don't see any reason to close this as off topic. Mathematica has a function to deal with problems like this(Orthogonalize), so to me it looks like a fine Mathematica topic. –  Sjoerd C. de Vries Jul 2 '13 at 20:22
show 5 more comments

1 Answer 1

up vote 3 down vote accepted

Based on the Wikipedia article you referred, here is a code

u[1] = HermiteH[1, x];
Do[
  u[n] = HermiteH[n, x] - Sum[Integrate[HermiteH[n, x] u[i], 
  {x, -1.0, 1.0}], {i, 1,n-1}], {n, 2, 45}
]; 
share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.