Derivatives of Computable Functions

✍ Scribed by Ning Zhong

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 665 KB
• Volume: 44
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19980440303

✦ Synopsis

Abstract

As is well known the derivative of a computable and C^1^ function may not be computable. For a computable and C∞ function f, the sequence {f^(n)^} of its derivatives may fail to be computable as a sequence, even though its derivative of any order is computable. In this paper we present a necessary and sufficient condition for the sequence {f^(n)^} of derivatives of a computable and C^∞^ function f to be computable. We also give a sharp regularity condition on an initial computable function f which insures the computability of its derivative f′.