rewriting a piecewise equation as a non-piecewsie equation: odd and even

Question

I would like to write the equation, $$I=\begin{cases} k & N \text{ even} \\ 0 & N \text{ odd} \end{cases}$$ as a function of $N$ in a non-piecewise format.

Any guidance/suggestions would be appreciated.

If you need to smoothly interpolate between the reals, $I=k\cos^2\left(\frac{\pi N}{2}\right)$ should work as well. — Graviton, Feb 13 '22 at 03:26

score 1 · Accepted Answer · answered Feb 13 '22 at 03:21

1

$$I = \frac{k\left(1+(-1)^N\right)}{2} $$

answered Feb 13 '22 at 03:21

blamocur

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rewriting a piecewise equation as a non-piecewsie equation: odd and even

1 Answers1