اريد مساعدة ضرووووري في حل مسائل في طرق نظرية دالة جرين

[أ. دلال]

This problem concerns the Green’s function for the Helmholtz equation in two dimensions, with
outgoing-wave boundary conditions.
(a) Use an eigenfunction expansion to show that the Green’s function is in terms of a Hankel function.
[You will need to evaluate some integrals. Look them up in a table of integrals or in Mathematica.]
(b) Derive the Green’s function by rst solving the Helmholtz equation away from the source point
and then normalizing [as we did in class for the Laplace equation Green’s function].