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A complex function that interpolates the Dunkl factorial
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DOI：10.1080/10652469.2025.2567001.png)
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Abstract
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In the Dunkl context (on the real line) with parameter nu>-1, the role of the ordinary exponential function exp(z)=& sum;(infinity)(n=0)z(n)/n! is played by the Dunkl exponential function E-nu(z)=& sum;(infinity)(n=0)z(n)/gamma(n,nu), for certain sequence gamma(n,nu)(depending on nu), in such a way that gamma n,-1/2=n! and E-1/2(z)=exp(z). The gamma function is a complex function that interpolates the factorial, i.e. it satisfies Gamma(n+1)=n!. In this paper, we look for a suitable complex function Gamma(nu)(z) that satisfies Gamma(nu)(n+1)=gamma(n,nu), and study its properties
Keywords:
Gamma function
Dunkl exponential function
Dunkl factorial
Bessel functions
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