Dear RG members,

I have a doubt in my derivation of Bessel functions and modified Bessel functions of asymptotic expansions in the limit zero.

When I derive the asymptotic expansion of x*J'(m,x)/J(m,x) in the limit x tends to 0 for all m>0 I have the value m and in the modified Bessel functions

x*K'(m,x) /K(m,x) in the limit x tends to zero for all m>0 I have the value  -m

I just want to know whether this values are correct or not.

In each of the above Bessel function numerator involving a first derivative.  

Thanking you