On a Theorem of T. Gneiting on [alpha]-Symmetric Multivariate Characteristic Functions

T. Gneiting (1998, J. Multivariate Analysis64, 131-147) proved a relation between the primitives of the classes [Phi]d(2) and [Phi]d(1) of 2- and 1-symmetric characteristic functions on d, respectively. We will give a straightforward proof of his relation, answering a question of his. To do this we use the calculus of generalized hypergeometric functions.