Theory of Bessel Functions of High Rank - I: Fundamental Bessel   Functions
  In this article we introduce a new category of special functions called fundamental Bessel functions arising from the Voronoi summation formula for $\mathrm{GL}_n (\mathbb{R})$. The fundamental Bessel functions of rank one and two are the oscillatory exponential functions $e^{\pm i x}$ and the classical Bessel functions respectively. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel equations. 
Zhi Qi
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