June 2017 Archives

Further On A Calculus Of Differences

As I have previously reported, my fellow students and I have found our curiosity drawn to the calculus of sequences, in which we define analogues of the derivatives and integrals of functions for a sequence sn with the operators

  Δ sn = sn - sn-1

and
  n
  Δ-1 sn = Σ si
  i = 1
respectively, where Σ is the summation sign, for which we interpret all non-positively indexed elements as zero.

I have already spoken of the many and several fascinating similarities that we have found between the derivatives of sequences and those of functions and shall now describe those of their integrals, upon which we have spent quite some mental effort these last few months.

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