= Symmetric second derivative
{title2=$D_s^2F(t)=\lim_{h\to0}[F(t+h)-2F(t)+F(t-h)]/h^2$}
The symmetric second derivative is the displayed limit when it exists. For a twice continuously differentiable function it equals the ordinary second derivative by Taylor expansion; the definition itself does not require ordinary differentiability. A <continuous function> with vanishing symmetric second derivative throughout an interval must be affine, by <vanishing symmetric second derivative forces an affine function>. For a twice-integrated Fourier series, sinc-squared weights express this quotient, connecting the operation to <Riemann summation of a convergent trigonometric series>.
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