Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633889 | Applied Mathematics and Computation | 2008 | 9 Pages |
Abstract
We obtain a new asymptotic expansion of generalized Fresnel integrals x(t)=∫0tcosq(s)ds for large t , where q(s)∼spq(s)∼sp when s→∞s→∞, and p>1p>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)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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Luka Korkut, Domagoj Vlah, Darko Žubrinić, Vesna Županović,