The mathematical foundations of the asymptotic iteration method
| العنوان: | The mathematical foundations of the asymptotic iteration method |
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| المؤلفون: | Davide Batic, Marek Nowakowski |
| المصدر: | Mathematical Methods in the Applied Sciences. 46:10833-10849 |
| بيانات النشر: | Wiley, 2023. |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Mathematics - Classical Analysis and ODEs, General Mathematics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, General Engineering, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Mathematical Physics (math-ph), General Relativity and Quantum Cosmology, Mathematical Physics |
| الوصف: | We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the approximants. With the help of this alternative termination condition and certain properties of continuous fractions, we derive a closed formula for the asymptotic function $\alpha$ of the AIM technique in terms of an infinite series. Furthermore, we show that such a series converges pointwise to $\alpha$ which, in turn, can be interpreted as a specific term of the minimal solution of a certain recurrence relation. We also investigate some conditions ensuring the existence of a minimal solution and hence, of the function $\alpha$ itself. Comment: 15 pages |
| تدمد: | 1099-1476 0170-4214 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c0d14f601ef6e7b21d5ded1ea6991bf7 https://doi.org/10.1002/mma.9154 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....c0d14f601ef6e7b21d5ded1ea6991bf7 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10991476 01704214 |
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