On a theorem of T. Gneiting on \(\alpha\)-symmetric multivariate characteristic functions (Q1840780)

\textit{T. Gneiting} [ibid. 64, No. 2, 131-147 (1998; Zbl 0904.60011)] proved a relation between the primitives of the classes \(\Phi_d(2)\) and \(\Phi_d(1)\) of 2- and 1-symmetric characteristic functions on \(\mathbb{R}^d\), respectively. The author of the paper under review gives a straightforward proof of his relation, answering a question of his. To do this, the author makes use of the calculus of generalized hypergeometric functions.