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| Titel: |
A Class of Functions with Removable Singularities and Their Application to the Physical Theory Of Diffraction |
| Auteur: |
Asvestas, John S. |
| Verschenen in: |
Electromagnetics |
| Paginering: | Jaargang 15 (1995) nr. 2 pagina's 143-155 |
| Jaar: |
1995-03-01 |
| Inhoud: |
We present a class of modified trigonometric functions that are related to repeated integrals of the cosine function. In their closed form, these functions have a removable singularity at the origin: they are not defined there but their limit exists and is finite. The presence of the singularity makes them computationally unstable in an interval about the origin. In this interval, however, we can represent them as alternating power series and, hence, we can compute them to any required accuracy. We use these functions to stabilize the computation of two expressions in the physical theory of diffraction. One is related to the wedge-diffraction coefficient and the other is Kirchhoff's integral over a polygon. Both of them are computationally unstable due to removable singularities. By re-writing them in terms of the new functions, we show that we can control their computation to any accuracy desired. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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