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arXiv · 2110.11555

The partial derivative of Okamoto's functions with respect to the parameter

Nathan Dalaklis·Kiko Kawamura·Tobey Mathis·Michalis Paizanis
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Abstract

The differentiability of the one parameter family of Okomoto's functions as functions of $x$ has been analyzed extensively since their introduction in 2005. As an analogue to a similar investigation, in this paper, we consider the partial derivative of Okomoto's functions with respect to the parameter $a$. We place a significant focus on $a = 1/3$ to describe the properties of a nowhere differentiable function $K(x)$ for which the set of points of infinite derivative produces an example of a measure zero set with Hausdorff dimension $1$.

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Nathan Dalaklis, Kiko Kawamura, Tobey Mathis, Michalis Paizanis. 2021-10-22. The partial derivative of Okamoto's functions with respect to the parameter. https://arxiv.org/abs/2110.11555

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