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I'm having to complete a piece of work for which I have to consider Bessel function quotients. By that I mean:

Kn'(x)/Kn(x) and In'(x)/In(x)

By Kn(x) I mean a modified Bessel function of the second kind of order n and by Kn'(x) I mean the derivative of Kn(x) with respect to the argument x.

Simurlaly, In(x) is a modified Bessel function of the first kind of order n and In'(x) is its derivative.

Basically what I need to find is Kn'(x)/Kn(x) and In'(x)/In(x) for x tending to zero, this obviously gives rise to a lot of "infinity/infinity" and "0/0" situations, so I need to perform some analysis on these.

My supervisor has suggested using a squeezing technique, which I think would work but would require upper and lower bounds of the quotients.

I know it's a bit of an involved question, but does anyone have any advice (I'm killing myself with this one!).

Thanks guys!