Discrete Calculus of Finite Sequences
  The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define convexity for finite sequences and some related concepts. To finalize, we propose a way to go from our extension to the calculus of finite differences. 
S\'ergio Martins Filho
cs.DM math.FA