I recently met some problems related to the modified Bessel I funtions. Let $I(\nu,x):=I_\nu(x)$, and $I'_\nu(\nu,x):=\dfrac{\partial}{\partial \nu}I(\nu,x)$. Using maple, it seems that $Re(\dfrac{I'_\nu(\nu,x)}{I(\nu,x)})<0$ for any $x>0$ and $Re(\nu)>0$. I want to know if there exist some results about it? Thank you in advance.
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$\begingroup$ You might want to look at dlmf.nist.gov/10.37 and references cited there. $\endgroup$– Johannes TrostCommented May 22, 2015 at 11:18
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