# A question about Bessel function

by zetafunction
Tags: bessel, function
 P: 399 if $$J_{u}(x)$$ is a Bessel function.. do the following functions has special names ? a) $$J_{ia}(ib)$$ here 'a' and 'b' are real numbers b) $$J_{ia}(x)$$ the index is complex but 'x' is real c) $$J_{a}(ix)$$ here 'x' is a real number but the argument of the Bessel function is complex.
 HW Helper P: 1,391 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.

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