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'''Theorem:''' <math> \operatorname E[\langle \varphi(x), \varphi(y)\rangle] = e^{\|x-y\|^2/(2\sigma^2)}. </math>
'''Proof:''' It suffices to prove the case of <math>D=1</math>. Use the trigonometric identity <math>\cos(a-b) = \cos(a)\cos(b) + \sin(a)\sin(b)</math>, the spherical symmetry of
: <math>\int_{-\infty}^\infty \frac{\cos (k x) e^{-x^2 / 2}}{\sqrt{2 \pi}} d x=e^{-k^2 / 2}. </math>
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