Special purpose differentiation algorithms

Abstract

The structure of SIGSAM Problem #8, [1], motivated the development of algorithms to determine an arbitrary, say r-th, derivative with respect to t of a function f(t) α , where [EQUATION]

A solution to SIGSAM problem #8

“…The structure of these proofs indicates however that, instead of the recursive definition of the ~'s as given in [2], in this case a closed form for these ~'s is preferable.…”

“…[I], is asked for a part of the power series expansion of The presented solution, based on special purpose differentiation algorithms [2], is constructed to give some insight in the structure of P (n). r A short summary of some notational conventions, used in [2], is necessary: The operators D and Z denote differentiation by t and replacement of t by 0, respectively.…”

“…r A short summary of some notational conventions, used in [2], is necessary: The operators D and Z denote differentiation by t and replacement of t by 0, respectively. Let ~ c IR~ {0, i, ... , r-l} and r E I.…”