Generalized Fresnel integrals and fractal properties of related spirals
作者:
Highlights:
•
摘要
We obtain a new asymptotic expansion of generalized Fresnel integrals x(t)=∫0tcosq(s)ds for large t, where q(s)∼sp when s→∞, and p>1. The terms of the expansion are defined via a simple iterative algorithm. Using this we show that the box dimension of the related q-clothoid, also called the generalized Euler or Cornu spiral, is equal to d=2p/(2p-1). Furthermore, this curve is Minkowski measurable, and we compute its d-dimensional Minkowski content. We also find oscillatory dimension of Fresnel integrals by studying the corresponding chirps.
论文关键词:Generalized Fresnel integrals,Generalized Euler or Cornu spiral,Chirp,Box dimension,Minkowski content
论文评审过程:Available online 13 September 2008.
论文官网地址:https://doi.org/10.1016/j.amc.2008.09.009