Estamos realizando la búsqueda. Por favor, espere...

Simple bounds with best possible accuracy for ratios of modified Bessel functions

Abstract: The best bounds of the form B (alfa, beta,gamma, x) = (alfa +beta2+gamma2x2)/x for ratios of modified Bessel functions are characterized: if alfa, beta and gamma are chosen in such a way that B (alfa, beta, gamma, x) is a sharp approximation for phi nu (x) =Iv-1x/Iv(x) as x -- 0+ (respectively x -- + infinito) and the graphs of the functions B (alfa, beta, gamma, x) and phi nu (x) are tangent at some x =xasterisco >0, then B (alfa, beta, gamma, x) is an upper (respectively lower) bound for phi nu (x) for any positive x, and it is the best possible at xasterisco. The same is true for the ratio phi nu (x) =K nu+1(x)/ K nu (x) but interchanging lower and upper bounds (and with a slightly more restricted range for nu). Bounds with maximal accuracy at 0+and +infinitoare recovered in the limits xasterisco --0+ and xasterisco -- +infinito, and for these cases the coefficients have simple expressions. For the case of finite and positive xasterisco we provide uniparametric families of bounds which are close to the optimal bounds and retain their confluence properties.

 Autoría: Segura J.,

 Fuente: Journal of Mathematical Analysis and Applications, 2023, 526(1), 127211

 Año de publicación: 2023

 Nº de páginas: 26

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2023.127211

 ISSN: 0022-247X,1096-0813

 Proyecto español: PGC2018-098279-BI00

 Url de la publicación: https://doi.org/10.1016/j.jmaa.2023.127211