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Two-sided bounds uniform in the real argument and the index for modified Bessel functions |
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| Authors: | B. V. Pal’tsev |
| Affiliation: | (1) Computer Center, Russian Academy of Sciences, USSR |
| Abstract: | Bounds uniform in the real argument and the index for the functionsa ν (x)=xI′ ν (x)/I′ ν (x) andb ν (x)=xK′ ν (x)/K ν (x), as well as for the modified Bessel functionsI ν(x) andK ν(x), are established in the quadrantx>0, ν≥0, except for some neighborhoods of the pointx=0, ν=0. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 681–692, May, 1999. |
| Keywords: | two-sided bounds Bessel function modified Bessel functions upper and lower barriers the differential inequality theorem |
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