I have to deal with Modified Bessel functions of the first kind frequently in my research. Here I list some useful properties of them for future reference.
$$I_0'(x) = I_1(x)$$
$$I_1'(x) = \frac{I_0(x)+I_2(x)}{2} $$
$$\frac{I_1(x)}{I_0(x)}\uparrow \Leftrightarrow I_0(x)(I_0(x …