besselj besseli for pure imaginary argument

Hi.

My question is about besselj and besseli.

besselj provides the solution of the Bessel equation:

(1)

while besseli provides the solution of the modified bessel equation:

(2)

Sometimes the Bessel equation is written in the form:

(3)

and the solution is . If q is a pure imaginary number, is also solution of the latter equation since:

(4)

When it comes to solve equation (3) for pure imaginary argument, it seems that several authors prefer to switch to the modified bessel equation

in order to solve (3). My question is if the convenience of that is in avoiding to hande imaginary argument or if I'm missing something else.

Could you please help?

[Jan]

Is the a relation to MATLAB in tis question?