This is about proof of orthogonality of spherical bessel functions
The book gave
For , and
I got only
Helmholtz equation: Where
Where is the Spherical Harmonics.
And (1) is the Spherical Bessel function.
Orthogonal properties stated that
For where is finite and :
For and
For and (2)
And (3) where is the j zero of the Bessel function.
Here is my work:
For , and
As the two have different independent variables and from (2),
Using (1), (3)
as is the zero of
I am missing an . Please help
Thanks
I already find proof that for where is finite and :
So all I need to proof is
But as in the last post:
as is the zero of
I am missing the . This time, it's a lot simpler and more focus, please help me on this.
Thanks