• #1
benorin
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Main Question or Discussion Point

0. Introduction
As for the reference material I have used the text Special Functions by Askey, Andrews, and Roy which covers much of the theorems here outlined. Another reference text, I cite Theory and Applications of Infinite Series by Knopp. As for original content I only have hope that the method of using the sets
$$C_N^n: = \left\{ {\vec x \in {\mathbb{R}^n}|{x_i} \ge 0\forall i,\sum\limits_{k = 1}^n {x_k^{2N}}  < n – 1} \right\}$$
and Dirichlet integrals to evaluate the integrals
$$\mathop {\lim }\limits_{N \to \infty } \int\limits_{C_N^n} {f\left( {\vec x} \right)d\mu }  = \int\limits_{{{\left[ {0,1} \right]}^n}} {f\left( {\vec x} \right)d\mu }$$
might be original material as I have never seen it my reading though there is nothing new under...
Continue reading...
 

Answers and Replies

  • #2
mathman
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Do you have a specific question? ##\lim_{N\to \infty} C_N^n=[0,1)## is straightforward.
 
  • #3
benorin
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Yes, it is, I had used that particular definition of ##C_N^n## with the ##\leq n-1## (opposed to ##\leq n##) to accommodate and singular point of an a few integrands in section 4, whereas the latter would converge to ##\left[ 0,1\right]##. These two definitions cover all of the integrals in the text.
 
  • #4
benorin
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I updated the Insight to include more exercises in sections 4 and 5 and added a few answers to section 1 at the end.
 

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