【摘 要】
：
We consider fractional Fuss-Catalan numbers C(k,l,n),n=0,1,….for fractional values of parameter in the form k/l,with k end l positive integers.We furnish e
【机 构】
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UniversityPierreetMarieCurie(Paris-Ⅵ),France
【出 处】
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The XXIX International Colloquium on Group-Theoretical Metho
论文部分内容阅读
We consider fractional Fuss-Catalan numbers C(k,l,n),n=0,1,….for fractional values of parameter in the form k/l,with k end l positive integers.We furnish exact solution of the Hausdorff moment problem,with C(k,l,n) as nth moment of a positive function W(k,l,x) which can be expressed explicitly as a finite sum of hypergeometric functions.We cite instances when W(k,l,x) are expressible via elementary functions.The functions W(k,l,x) are studied analytically and graphically.These results are discussed in the perspective of the free probabilities,where the functions W(k,l,x) are shown to be equal to free fractional powers of the standard Marchenko-Pastur distribution.
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