A question about Bessel function

by zetafunction
Tags: bessel, function
zetafunction is offline
Dec18-12, 04:05 AM
P: 399
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.
Phys.Org News Partner Science news on Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior
Mute is offline
Dec18-12, 08:24 AM
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.

Register to reply

Related Discussions
Question on complex integration involving Bessel Function and essential Singularities Calculus 1
Using Bessel generating function to derive a integral representation of Bessel functi Calculus & Beyond Homework 3
Question on zeros of a Bessel function. Differential Equations 8
Expansion of free space Green function in Bessel function Advanced Physics Homework 0
Bessel function and Bessel D.E. Calculus 22