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Author of this book i am reading claims that the nth factor of $\frac {1\cdot 2\cdot 3\cdots( m-1) } {( z+1)( z+2) \cdots( z+m-1) }m^{s}$ is $\frac {n} {z+n}( \frac {n+1} {n}) ^{s}$ shouldn't it be just $\frac {n} {z+n}( n+1) ^{s} ?$

Edit: The author claims the product would look like $\prod _{n=1}^{n=m-1}\frac {n} {z+n}\left( \frac {n+1} {n}\right) ^{s}.$ I think (most likely incorrectly) that it should be written as $\prod _{n=1}^{n=m-1}\frac {n} {z+n}\left({n+1} \right) ^{s}$

i think i can see my mistake so i am going to close the post.

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    @Arturo Thanks i did n't not double dollars put the equations on new lines. I have been meaning to find out how to accomplish that.2012-03-05

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The author is right.

What your product gives us is

$\dfrac {1.2.3\ldots \left( m-1\right) } {\left( z+1\right) \left( z+2\right) \ldots \left( z+m-1\right) }(m!)^{s}$

Note that it is $(m!)^s$ and not $m^s$.

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    @Hardy: You are welcome. Mistakes are the best way to learn! So don't be embarrassed.2012-03-05