Shranjeno v:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Izdano: |
2001
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| Teme: | |
| Online dostop: | https://arxiv.org/abs/math/0109187 |
| Oznake: |
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Kazalo:
- Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/π$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain non-oscillating integrals for complex values of $z$. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.