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Uniform (very) sharp bounds for ratios of parabolic cylinder functions

Abstract: Parabolic cylinder functions are classical special functions with applications in many different fields. However, there is little information available regarding simple uniform approximations and bounds for these functions. We obtain very sharp bounds for the ratio [ ...] and the double ratio [...] in terms of elementary functions (algebraic or trigonometric) and prove the monotonicity of these ratios; bounds for [...] are also made available. The bounds are very sharp as [...] and this simultaneous sharpness in three different directions explains their remarkable global accuracy. Upper and lower elementary bounds are obtained which are able to produce several digits of accuracy for moderately large [X] and/or n.

 Autoría: Segura J.,

 Fuente: Studies in Applied Mathematics, 2021, 147(2), 816-833

 Editorial: Blackwell Publishing Ltd

 Fecha de publicación: 01/08/2021

 Nº de páginas: 18

 Tipo de publicación: Artículo de Revista

 DOI: 10.1111/sapm.12401

 ISSN: 0022-2526,1467-9590

 Proyecto español: PGC2018-098279-B-I00

 Url de la publicación: https://doi.org/10.1111/sapm.12401