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.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 681–692, May, 1999.
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Pal’tsev, B.V. Two-sided bounds uniform in the real argument and the index for modified Bessel functions. Math Notes 65, 571–581 (1999). https://doi.org/10.1007/BF02743167
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DOI: https://doi.org/10.1007/BF02743167