Original function

Transformed function

$u\left(x\right)=u_1\left(x\right)\pm u_2\left(x\right)$

$U\left(k\right)=U_1\left(k\right)\pm U_2\left(k\right)$

$u\left(x\right)=cv\left(x\right)$

$U\left(k\right)=cV\left(k\right)$

$u\left(x\right)=u_1\left(x\right)u_2\left(x\right)$

$U\left(k\right)={\displaystyle \sum _{m=0}^k{U}_1\left(m\right)U_2\left(k-m\right)}$

$u\left(x\right)=\frac{{\partial }^{k}v\left(x\right)}{\partial x^k}$

$U\left(k\right)=\frac{\left(k+m\right)!}{k!}V\left(k+m\right)$