Functions with derivatives given by polynomials in the function itself or a related function

dc.contributor.author	Franssens, G.R.
dc.date	2007
dc.date.accessioned	2016-09-26T12:14:18Z
dc.date.available	2016-09-26T12:14:18Z
dc.identifier.uri	https://orfeo.belnet.be/handle/internal/4365
dc.description	We construct the set of holomorphic functions S 1 = {f: Ω f ⊆ ℂ → ℂ} whose members have n-th order derivatives which are given by a polynomial of degree n+1 in the function itself. We also construct the set of holomorphic functions S 2 = {g: Ω g ⊆ ℂ → ℂ} whose members have n-th order derivatives which are given by the product of the function itself with a polynomial of degree n in an element of S 1. The union S 1 ∪ S 2 contains all the hyperbolic and trigonometric functions. We study the properties of the polynomials involved and derive explicit expressions for them. As particular results, we obtain explicit and elegant formulas for the n-th order derivatives of the hyperbolic functions tanh, sech, coth and csch and the trigonometric functions tan, sec, cot and csc.
dc.language	eng
dc.relation.ispartofseries
dc.title	Functions with derivatives given by polynomials in the function itself or a related function
dc.type	Article
dc.subject.frascati	Mathematics
dc.audience	Scientific
dc.source.title	Analysis Mathematica
dc.source.volume	33
dc.source.issue	1
dc.source.page	17-36
Orfeo.peerreviewed	Yes
dc.identifier.doi	10.1007/s10474-007-0102-5
dc.identifier.scopus	2-s2.0-33847407138