All Questions
8 questions
3
votes
1
answer
112
views
Error in Creating Orthogonal Polynomials
I'm trying to create my own set of polynomials orthogonal to weight $w(x)=x^{14}$ on $[-a,a]$. My code:
...
- 231
3
votes
1
answer
73
views
Non-Convergence In Creating Legendre Series
I'm trying to use Mathematica to create a Legendre-Fourier series using this Wikipedia article. Here is my code:
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- 231
4
votes
2
answers
394
views
How to check whether Laguerre polynomials are orthogonal?
I've got the problem with checking if Laguerre polynomials for n=1,...,10 are orthogonal.
I have to create the list of these polynomials, then create the matrix of integrals from 0 to infinity. ...
- 41
0
votes
0
answers
82
views
Integration involving Hermite polynomials [duplicate]
I having trying to evaluate Integrate[Exp(-x^2 - k x) Hermite[n,x]Hermite[m,x], {x,-Inf,Inf}] without any success. Does anyone know either how to do it or what is the result of it? Any help would be ...
- 11
3
votes
1
answer
2k
views
Integrate Squared Legendre Polynomial
With the same purpose as this question, I wish to evaluate an integral that contains the squared Legendre Polynomials.
$\int_{-1}^{1}\left[P_n(x)\right]^2dx=\frac{2}{2n+1}$
I tried evaluating with ...
- 155
3
votes
0
answers
497
views
Integrating the Associated Legendre Polynomials
I know the following identity:
$\qquad \int_{-1}^1 P_l^m(t)^2dt=\frac{2(m+n)!}{(2n+1)(n-m)!}$
I would like to verify this result using Mathematica. This is what I entered:
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- 131
3
votes
1
answer
423
views
Mathematica is unreliable about recognizing orthogonal functions
Hermite polynomials should be orthogonal over a Gaussian measure. However when the orders of the polynomials are larger than a few, Mathematica gets this wrong. Strangely, it seems to hinge on whether ...
- 31
4
votes
2
answers
1k
views
How do I evaluate a symbolic integral involving Hermite polynomials?
I want to test a difficult integral : Integral on all reals of some complicated function involving the Hermitian polynomials, exponentials, squares, factorials, and being general considering any ...
- 63