Discrete analogues of the classical Fourier-Jacobi transform are introduced and investigated. It involves series and integrals with respect to parameters of the Gauss hypergeometric function ${}_2{F}_1(a+in/2,a-in/2;c;-x^2),x>0,n\in \mathbb{N},a,c>0,i$ is the imaginary unit. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established.

中文翻译：

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离散傅里叶-雅可比变换

介绍并研究了经典傅里叶-雅可比变换的离散类似物。它涉及关于高斯超几何函数参数的级数和积分${}_2{F}_1(\mathrm{一个}+\mathrm{一世}n/2,\mathrm{一个}-\mathrm{一世}n/2;C;-X^2),X>0,n\in \mathbb{ñ},\mathrm{一个},C>0,\mathrm{一世}$是虚数单位。根据这些级数和积分，建立了适合函数和数列的相应反演公式。