Odd Function

$$\mathbb{O}(x)=\frac{f(x)-f(-x)}{2}$$ $$\mathbb{O}(-x)=-\mathbb{O}(x)$$ $$\int f(t)\mathbb{O}(t)dt=\int f_{\mathbb{O}}(t)\mathbb{O}(t)dt$$

• Sum of odd functions is odd
• Sum of odd functions is an Even Function
• Product of an even and odd is an Odd Function