# Confused on Bessel Proof

1. Oct 13, 2009

### Void123

1. The problem statement, all variables and given/known data

Prove J(-m) = [(-1)^m][J(m)]

(Note: by "J(-m)" I mean "subscript (-m)")

2. Relevant equations

J(-m) = sum [((-1)^n) * (x/2)^(2n-m)]/[n! $$\Gamma$$(n - m + 1)]

J(m) should be obvious.

3. The attempt at a solution

I tried just plugging in the above formulas hoping to get a simplified answer, but I know I'm missing something in that denominator.

2. Oct 13, 2009

### lanedance

is m an integer?

maybe try showing your working & what special properties of the gamma function can you use to help?

3. Oct 13, 2009

### Void123

Yes, m is an integer. I am also told that $$\Gamma (-k) = \infty$$ and that I should, therefore, eliminate the terms from the sum that equal zero. Also, 1/[(2^m)($$\Gamma$$ (m + 1))] is reduced to some 'a' constant.

That's all I got.

Not entirely sure what to do.

4. Oct 13, 2009

### Void123

I think I figured it out.

5. Oct 13, 2009

### lanedance

cool, yeah its true that for negative integers
$$|\Gamma (-k)| \rightarrow \infty$$
the other handy ones were for integers:
$$\Gamma (n) = (n-1)!$$
and so
$$\Gamma (n+1) = n \Gamma(n)$$