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I How is it that the SPH cubic spline kernel in normalized?

  1. Mar 22, 2017 #1
    Hi,

    (This is more of a math question but I thought Astronomy people would be more familiar with the equation and how it's used)
    So in Monaghan 1992 (http://adsabs.harvard.edu/abs/1992ARA&A..30..543M, bottom of pg 554) a cubic spline in three dimensions is defined. I tried to integrate it (using a triple integral in spherical coordinates), expecting to get 1 but got ##3\pi/4h^2##. Are there special considerations that need to be taken into account when your integrating this function? Here's my work:

    kernel_integral_1.jpg

    kernel_integral_2.jpg

    (I tried to make the writing easier to see by fiddling with the contrast, it kind-of worked)
    (Also, I'm an Undergrad doing research so I didn't know what level to make the thread ... I or A ... )

    Thanks,
    - Andrew
     
  2. jcsd
  3. Mar 28, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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