Are bessel functions pure real?

[Pacopag]

Homework Statement

I'm wondering if the bessel functions are pure real. What I really want to know is that if the bessel funtions are $$J$$ and $$Y$$ (i.e. first and second kinds), and the Hankel functions are
$$H_1=J+iY$$ and $$H_2=J-iY$$, then can we say that
$$H_1=H_{2}^{*}$$ where the * denotes complex conjugation?

Note that I'm considering the case where the bessel functions have real arguments.

Homework Equations

The Attempt at a Solution

 

[Dick]

http://en.wikipedia.org/wiki/Bessel_function#Bessel_functions_of_the_first_kind_:_J.CE.B1

While they may not say explicitly that they are real, look at the power series expansion for real x.

 

[Pacopag]

Great. Thanks.