A question about Bessel function

zetafunction

if [tex] J_{u}(x) [/tex] is a Bessel function..

do the following functions has special names ?

a) [tex] J_{ia}(ib) [/tex] here 'a' and 'b' are real numbers

b) [tex] J_{ia}(x) [/tex] the index is complex but 'x' is real

c) [tex] J_{a}(ix) [/tex] here 'x' is a real number but the argument of the Bessel function is complex.

Mute

Bessel functions ##J_\nu(z),~Y_\nu(z)## of real order and imaginary argument are related to the modified Bessel functions ##I_\nu(z),~K_\nu(z)## in a similar way as sine and cosine are related to sinh and cosh.

For imaginary order, see this Bessel function subpage on the Digital Library of Mathematical functions; for imaginary order and imaginary argument (i.e., the modified Bessel functions of imaginary order), see this page.