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We provide detailed algebra for determining the integrated mean-squaredprediction error (IMSPE) of designs of computer experiments, with one factorand one or two points, under the exponential, Gaussian, or either of two Materncorrelation functions. This algebra shall provide the basis for theidentification of the IMSPE as a member of a special class oflow-degree-truncated rational functions, which we name, here, the Nu class. Weshall detail this function class in a series of papers, of which this is thefirst.

The Nu Class of Low-Degree-Truncated, Rational, Generalized Functions.  I. IMSPE in Design of Computer Experiments: Integrals and Very-Low-N,  Single-Factor, Free-Ranging Designs