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Introduction

This bit is what new thing you can learn reading this:) 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 certain integrals of the type

$$\mathop {\lim }\limits_{N \to \infty } \int\limits_{C_N^n} {f\left( {\vec x} \right)d\mu } = \int\limits_{{{\left[ {0,1} \right]}^n}} {f\left( {\vec x} \right)d\mu }$$

might be original material as I have never seen it my reading.

Summary

The main purpose of this paper is to derive the formulas in Sections 4 and 5. Section 4 hold n-fold iterated integral representations of some special functions (where n is a positive integer), though somewhat dense, all the material up to this and including Section 3 is just advanced Calc 3 level material; Sections 4&5 are the analysis content, section 5 contains fractional integrals as analytic...

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