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How to solve a vector integral within a solid angle ?

• To: mathgroup at smc.vnet.net
• Subject: [mg128281] How to solve a vector integral within a solid angle ?
• From: Seila Ancientmoon <seilaancientmoon at gmail.com>
• Date: Wed, 3 Oct 2012 23:39:55 -0400 (EDT)
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hi,
I want to plot a picture like Figure 5 in this paper and i need to calculate a function that present at page 8, the H(S) function:
http://users.tricity.wsu.edu/~bobl/personal/mypubs/1993_plausible.pdf
That integration take vector as parameters and integral over a hemisphere range, i want to ask is there a neat statement to do this integral rather than converting it to spherical coordinate than do the integration ?

Thanks.