Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments
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| Format: | Preprint |
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2004
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| _version_ | 1866914099700432896 |
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| author | Gil, Amparo Segura, Javier Temme, Nico M. |
| author_facet | Gil, Amparo Segura, Javier Temme, Nico M. |
| contents | We describe a variety of methods to compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $x^2 w'' +x w' +(a^2 -x^2)w=0$. In an accompanying paper (Algorithm xxx: Modified Bessel functions of imaginary order and positive argument) we describe the implementation of these methods in Fortran 77 codes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0401128 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments Gil, Amparo Segura, Javier Temme, Nico M. Numerical Analysis Classical Analysis and ODEs 33C10; 65D20 We describe a variety of methods to compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $x^2 w'' +x w' +(a^2 -x^2)w=0$. In an accompanying paper (Algorithm xxx: Modified Bessel functions of imaginary order and positive argument) we describe the implementation of these methods in Fortran 77 codes. |
| title | Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments |
| topic | Numerical Analysis Classical Analysis and ODEs 33C10; 65D20 |
| url | https://arxiv.org/abs/math/0401128 |