Examinando por Autor "Pablo Martin"

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  • Miniatura
    Ítem
    Accurate Analytical Approximation for the Bessel Function J2(x)
    (2024) Pablo Martin; Juan Pablo Ramos Andrade; Fabián Caro Pérez; Freddy Lastra
    We obtain an accurate analytic approximation for the Bessel function 𝐽2(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 𝐽2(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 𝜀rel=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.
  • Miniatura
    Ítem
    Description of Parameter Variation Learning with Artificial Intelligence and GeoGebra in Students of a Differential Equations Course
    (2024) Jorge Olivares Funes; Elvis R. Valero Kari; Pablo Martin
    In this era of social and technological change, the advent of AI has had great impact on the lives of many people and especially in the educational field, as mentioned in [1], wich prove that the perceptions that students and instructors have about artificial intelligence are very positive to implement them in learning. In this [2] assert that it is possible to have a collaborations between the fields of mathematics and artificial intelligence AI.