Example: Hankel Functions of the First and Second Kind
Show the relationship between Hankel functions H1 and H2 with Bessel functions Jn and Yn. Also show the relationships between these functions and their scaled versions.
The Hankel functions are not defined at 0.
1. Use symbolic evaluation to show the relationship between H1, Jn, and Yn.
2. Use symbolic evaluation to show the relationship between H2, Jn, and Yn.
◦ The real components of H1 and H2 are identical in value and sign.
◦ The imaginary components of H1 and H2 are identical in value but opposite in sign.
3. Note these two other important relationships between H1 and H2.
4. Create a plot to visually show that |H1|=|H2|.
5. Create a plot to show the relationship between H1, Jn and Yn.
6. Use symbolic evaluation to show the relationship between the Hankel functions and their scaled version.
7. Create a plot to show that:
8. Create a plot to show that:
