| Autor: |
Martin, Pablo, Ramos-Andrade, Juan Pablo, Caro-Pérez, Fabián, Lastra, Freddy |
| Předmět: |
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| Zdroj: |
Mathematical & Computational Applications; Aug2024, Vol. 29 Issue 4, p63, 8p |
| Abstrakt: |
We obtain an accurate analytic approximation for the Bessel function J 2 (x) using an improved multipoint quasirational approximation technique (MPQA). This new approximation is valid for all real values of the variable x, with a maximum absolute error of approximately 0.009. These errors have been analyzed in the interval from x = 0 to x = 1000 , and we have found that the absolute errors for large x decrease logarithmically. The values of x at which the zeros of the exact function J 2 (x) and the approximated function J ˜ 2 (x) occur are also provided, exhibiting very small relative errors. The largest relative error is for the second zero, with ε rel = 0.0004 , and the relative errors continuously decrease, reaching 0.0001 for the eleventh zero. The procedure to obtain this analytic approximation involves constructing a bridge function that connects the power series with the asymptotic approximation. This is achieved by using rational functions combined with other elementary functions, such as trigonometric and fractional power functions. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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