In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive these coefficients relies heavily upon known asymptotic results for hypergeometric functions and the final result shows that they can be expressed in closed form as a multiple of a certain $_{3}F_{2}$ hypergeometric function. Using the closed form expressions we are able to provide the precise asymptotic rates of decay for the spherical Fourier coefficients which we observe have a close connection to the asymptotic decay rate of the corresponding Euclidean Fourier transform.

翻译：在本文中,我们计算了将通用Wendland函数从美元-美元维维特欧几里德空间限制到(d-1)维维特单位域的球形Fourier扩展系数。得出这些系数所需的发展在很大程度上依赖于超地球函数的已知微量结果,最后结果显示,这些系数可以以封闭形式表示为一定的 $3}F ⁇ 2}超地球函数的倍数。使用封闭形式的表达式,我们能够为我们观察到的与相应的Euclidean Fourier变形的无源衰变率密切相关的球形四里欧系数提供精确的无源衰减率。