my aim is to interpolate a function like this: I have      |<--- h -->|<-------- k ----------->|          o----------o------------------------o    x(i-1)      x(i)                   x(i+1)with respective values $f(x_i-h), f(x_i), f(x_i+k)$, now I want to approximate $f(x+k/2)$ using centered formula.I know for example that $f(x+k/2)\approx \frac{f(x_i)+f(x_i+k)}{2}$ but what if I want to use also $f(x-h)?$thanks!
Interpolation over an unequally spaced grid
interpolation