Results 1 to 11 of 11

Math Help - Hermite Polynomials

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    51

    Hermite Polynomials

    how do I calculate the first three Hermite Polynomials ?

    thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by iLikeMaths View Post
    how do I calculate the first three Hermite Polynomials ?

    thank you
    Start by reading the following:

    Hermite polynomials - Wikipedia, the free encyclopedia

    Hermite polynomials: Definition from Answers.com

    http://kiwi.atmos.colostate.edu/grou...rmitePolys.pdf

    Hermite Polynomial

    Hermite polynomials - ALGLIB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2008
    Posts
    51
    thanks for the link, so the polynomials are
    • 1
    • 2x
    • 4x^2 - 2 etc
    I know that they are orthogonal but how do I prove/verify that they are?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by iLikeMaths View Post
    thanks for the link, so the polynomials are
    • 1
    • 2x
    • 4x^2 - 2 etc
    I know that they are orthogonal but how do I prove/verify that they are?

    Thanks
    Read the links carefully, do a little more research and see if you can find a proof. If you turn up nothing I'll post a proof in due course (but I'm betting you'll turn up something).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2008
    Posts
    51
    ive got to the point where i am integrating
    1 and 2x and the weighting function e^x^-2 (sori i dont know how to use LaTex) between the intervals infinity and minus infinity but i dont understand how the integral equals to zero if the intervals do not have a value. i have integrated the polynomials and i got -e^x^-2, hope you understand thanks
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by iLikeMaths View Post
    ive got to the point where i am integrating
    1 and 2x and the weighting function e^x^-2 (sori i dont know how to use LaTex) between the intervals infinity and minus infinity but i dont understand how the integral equals to zero if the intervals do not have a value. i have integrated the polynomials and i got -e^x^-2, hope you understand thanks
    To solve \int_{-\infty}^{+\infty} (1) (2x) e^{-x^2} \, dx make the substitution u = -x^2 and deal with the improper integral in the usual way (have you been taught about improper integrals and how to treat them?).
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by mr fantastic View Post
    To solve \int_{-\infty}^{+\infty} (1) (2x) e^{-x^2} \, dx make the substitution u = -x^2 and deal with the improper integral in the usual way (have you been taught about improper integrals and how to treat them?).
    Or just note that the integrand 2xe^{-x^2} is an odd function, and hence :
    \int_0^\infty 2xe^{-x^2} ~ dx=-\int_{-\infty}^0 2xe^{-x^2} ~ dx

    Since \int_{-\infty}^{\infty}=\int_0^\infty+\int_{-\infty}^0, the integral is 0.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Dec 2008
    Posts
    51
    i still dont understand , can i post the actual question because i think i am not explaining the question properly
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by iLikeMaths View Post
    i still dont understand , can i post the actual question because i think i am not explaining the question properly
    What do you not understand in post #6?

    Please feel free to post the actual question.

    It looks to me like you will need to revise and consolidate some of the background mathematics that your question expects you to understand and use.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Dec 2008
    Posts
    51
    [LEFT]The Actual Question

    Using the definition of orthogonality, verify that the polynomials found in
    1.(i.e. 1,2x, 4x^2 -2[FONT=CMR12])are mutually
    orthogonal. You may use the following integrals without proof
    \int_{-\infty}^{\infty}e^{-x^2}~dx = \sqrt\pi

    i think my actual problem is that i missed the class on this topic and i am totally confused, the book i am using is showing me a different way to do it, if you could please explain in a very simple way, thanks
    Last edited by iLikeMaths; December 14th 2008 at 03:34 PM.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by iLikeMaths View Post
    The Actual Question


    Using the definition of orthogonality, verify that the polynomials found in 1.(i.e. 1,2x, 4x^2 -2)are mutually
    orthogonal. You may use the following integrals without proof
    Orthogonal with respect to

    1. The weighting function e^{-x^2}

    2. over the interval -\infty < x < + \infty

    ???

    One of the required calculations has already been shown to you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Hermite polynomials
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 1st 2011, 07:29 PM
  2. An integral involving Hermite polynomials
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 20th 2010, 02:30 AM
  3. Hermite polynomials.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 24th 2010, 01:27 PM
  4. Error approximation (hermite)
    Posted in the Calculus Forum
    Replies: 0
    Last Post: July 29th 2009, 03:42 AM
  5. Hermite Polynomials
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: May 5th 2007, 07:43 PM

Search Tags


/mathhelpforum @mathhelpforum