On the solutions of second order difference equations with variable coefficients
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866910314755260416 |
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| author | Kadyrov, Shirali Orynbassar, Alibek |
| author_facet | Kadyrov, Shirali Orynbassar, Alibek |
| contents | In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are elementary and based on factoring a quadratic shift operator. As an application, we obtain two new generalized continued fraction formulas for the mathematical constant $π^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_03554 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the solutions of second order difference equations with variable coefficients Kadyrov, Shirali Orynbassar, Alibek Number Theory 39A06, 11J70 In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are elementary and based on factoring a quadratic shift operator. As an application, we obtain two new generalized continued fraction formulas for the mathematical constant $π^2$. |
| title | On the solutions of second order difference equations with variable coefficients |
| topic | Number Theory 39A06, 11J70 |
| url | https://arxiv.org/abs/2103.03554 |