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- Title
Fractional iteration of exponentially growing functions.
- Authors
Szekeres, G.
- Abstract
The fractional iteration of ex and solutions of the functional equation have frequently been discussed in literature. G. H. Hardy has shown (in [3], and in greater detail in [4]) that the asymptotic behaviour of the solutions of (1) cannot be expressed in terms of the logarithmico-exponential scale, although they are comparable with each member of the scale.1 Hence solutions of (1) provide a remarkably simple instance of functions whose manner of growth does not fit into the scale of L-functions but requires non-elementary orders of infinity for an accurate representation. This raises quite naturally the question whether there exists a most regularly growing solution of equation (1) which might serve as a prototype for this kind of growth. In a slightly more general context we may ask whether there exists a ‘best’ family of fractional iterates fσ(x), satisfying.
- Publication
Journal of the Australian Mathematical Society, 1962, Vol 2, Issue 3, p301
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788700026902