Start with .
Integrate the last term by parts, so that
.
For the second one, start with .
Thus (similar to the last part of the previous derivation).
Warning: the last identity is not quite the one given.
I have been given a modified Bessel function and it it defined by the integral
I have been asked to show that
(a)
(b)
Firstly i have started by trying to integrate the integral. Using and . Therefore and
Using integration by parts
I ended up with
knowing that
Therefore
I'm not sure if i'm on the right track to solving this problem. Any ideas of what i can do next? How do i then show that
(a)
(b)
I seem to be missing the from the result. I'm not sure where i might have gone wrong. I have checked it 3 times each different ways and i still keep getting the same answer.
I am using
which can be rewritten as which was prooven in the first part of this question.
Thus
And then i put the values in for and
and somehow i end up with the answer
Although it should be