Hypergeometric functions as a tool for summability of the Fourier integral
This paper is essentially a sequel to an earlier work by the first-named author and \textit{Y. Xu} [Math. Proc. Camb. Philos. Soc. 122, No. 1, 149-172 (1997; Zbl 0881.42007)] in which the so-called \(\ell-1\) summability of the inverse Fourier integral on \(\mathbb{R}^a\) was studied and a pair of Fourier kernels \(\{h_d,m_d\}\) on \(\mathbb{R}_+\) was introduced as the core of the summability scheme. In this paper, these same kernels are investigated once again from the point of view of special functions. The authors rederive several basic properties of these Fourier kernels. In particular, they derive a power series expansion verifying Ramanujan's master theorem.
scientific article; zbMATH DE number 1209930
scientific article