Original function
Transformed function
u ( x ) = u 1 ( x ) ± u 2 ( x )
U ( k ) = U 1 ( k ) ± U 2 ( k )
u ( x ) = c v ( x )
U ( k ) = c V ( k )
u ( x ) = u 1 ( x ) u 2 ( x )
U ( k ) = ∑ m = 0 k U 1 ( m ) U 2 ( k − m )
u ( x ) = ∂ k v ( x ) ∂ x k
U ( k ) = ( k + m ) ! k ! V ( k + m )