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Exact and explicit expressions for the variogram of first--order intrinsicautoregressions have not been known. Various asymptotic expansions andapproximations have been used to compute the variogram. In this note, an exactand explicit expression applicable for all parameter values is derived. Theexpression involves Appell's hypergeometric function of the fourth kind.Various particular cases of the expression are also derived.

Explicit expressions for the variogram of first-order intrinsic autoregressions