TABLE 1.

Special cases of Matérn covariance functions

	ν	h	$K_{\nu ,h,{\sigma }_K}\left({\mathbf{x}}_i,{\mathbf{x}}_j\right)$
Exponential	0.5	1	${\sigma }_K^2\cdot \exp \left(-\left|\right|{\mathbf{x}}_i-{\mathbf{x}}_j\left|\right|\right)$
	1.5	1	${\sigma }_K^2\cdot \exp \left(-\sqrt{3}\left|\right|{\mathbf{x}}_i-{\mathbf{x}}_j\left|\right|\right)\cdot \left(1+\sqrt{3}\left|\right|{\mathbf{x}}_i-{\mathbf{x}}_j\left|\right|\right)$
	2.5	1	${\sigma }_K^2\cdot \exp \left(-\sqrt{5}\left|\right|{\mathbf{x}}_i-{\mathbf{x}}_j\left|\right|\right)\cdot \left(1+\sqrt{5}\left|\right|{\mathbf{x}}_i-{\mathbf{x}}_j\left|\right|+\frac{5}{3}\left|\right|{\mathbf{x}}_i-{\mathbf{x}}_j|{|}^2\right)$
Gaussian	∞	1	$\exp \left(-\frac{1}{2}\left|\right|{\mathbf{x}}_i-{\mathbf{x}}_j|{|}^2\right)$