ABSTRACT
Like (9.09) this is a many valued function of z, unless v is an integer or zero. The principal branch is obtained by assigning (tz)' its principal value.
Comparing (9.09) with (10.01), we see that Iv (z) = e - v*f'2 Jv (iz), (10.02)
where the branches have their principal values when phz = 0, and are continuous elsewhere.' In consequence, Iv(z) is sometimes called the Bessel function of imaginary argument.