Two-sided bounds uniform in the real argument and the index for modified Bessel functions

Two-sided bounds uniform in the real argument and the index for modified Bessel functions

Bounds uniform in the real argument and the index for the functionsaν(x)=xI′ν(x)/I′ν(x) andbν(x)=xK′ν(x)/Kν(x), as well as for the modified Bessel functionsIν(x) andKν(x), are established in the quadrantx>0, ν≥0, except for some neighborhoods of the pointx=0, ν=0.

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Veröffentlicht in:Mathematical Notes 1999-05, Vol.65 (5), p.571-581
1. Verfasser: Pal’tsev, B. V.
Format: Artikel
Sprache:eng
Schlagworte:
Bessel functions
Mathematics
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Zusammenfassung:Bounds uniform in the real argument and the index for the functionsaν(x)=xI′ν(x)/I′ν(x) andbν(x)=xK′ν(x)/Kν(x), as well as for the modified Bessel functionsIν(x) andKν(x), are established in the quadrantx>0, ν≥0, except for some neighborhoods of the pointx=0, ν=0.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1007/BF02743167