# Sequence product

I'm trying to find a closed form expression for the following product: $$f(k) = \prod \limits_{m=1 \\m \neq k}^{N} \frac{1}{1-(\frac{k}{m})^{\alpha/2}}$$.

This can be simplified or approximated into: $$f(a) = \prod \limits_{m=1}^{N} \frac{1}{1-a \; m^{-\alpha/2}}$$.

A hint or an expression for either would be great. A limit when N tends to infinity can also be useful. Also, it would be helpful if there is any book with tables of products of sequences.

• Sorry for the typo, I corrected the question Oct 23 '18 at 14:54
• The condition $m \neq k$ should still be included in the "simplified" form Oct 23 '18 at 15:13