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Based on the geometry of the three difference quotients in calculus, it seems there should be a general form $$P(f(x + h) - f(x)) + (1 - P)(f(x) - f(x - h))\over h$$ where $0 <= P <= 1$, at least if $P$ is real.

Is there a name for this form, or any utility for it? Can $P$ ever be a non-real complex number?

user10478
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1 Answers1

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If $p=\frac{1}{2}$ then we arrive at the central difference. I did not see the approach you propose, however such differences could be called weighted differences.

szw1710
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