Results 1 to 4 of 4

Math Help - Simplification of Spherical Bessel functions

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    2

    Simplification of Spherical Bessel functions

    From here:



    Why isn't the (-x)^n (1/x)^n product simplified to (-1)^n?

    Thanks in advance for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,373
    Thanks
    48
    Quote Originally Posted by MrWaeseL View Post
    From here:



    Why isn't the (-x)^n (1/x)^n product simplified to (-1)^n?

    Thanks in advance for any help.
    Because it's an operator not just an algebraic expression. To demonstrate let n = 2 (and f(x) = \frac{\sin x}{x} ) so

     <br />
(-x)^2 \left(\frac{1}{x} \frac{d}{dx} \right)^2 f(x) = x^2 \frac{1}{x} \frac{d}{dx} \left(\frac{1}{x} \frac{df}{dx} \right) = \frac{d^2f}{d x^2} - \frac{1}{x} \frac{df}{dx}.<br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    2
    I see...so it would be wrong to state that \left(\frac{1}{x} \frac{d}{dx} \right)^n = (\frac{1}{x})^n (\frac{d}{dx})^n?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,373
    Thanks
    48
    Quote Originally Posted by MrWaeseL View Post
    I see...so it would be wrong to state that \left(\frac{1}{x} \frac{d}{dx} \right)^n = (\frac{1}{x})^n (\frac{d}{dx})^n?
    Absolutely. It only applies when n = 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Bessel's Functions
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 11th 2011, 01:14 AM
  2. zeros of bessel functions
    Posted in the Math Software Forum
    Replies: 0
    Last Post: June 29th 2011, 11:53 AM
  3. Bessel Functions Question
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: September 6th 2010, 07:49 PM
  4. Laplace transform of Bessel functions
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: January 23rd 2010, 05:00 AM
  5. Bessel Functions
    Posted in the Calculators Forum
    Replies: 1
    Last Post: August 16th 2007, 12:20 PM

Search Tags


/mathhelpforum @mathhelpforum