# Product of a serie

oscaralive
Hi all,
anyone knows how to compute the following serie?

\prod_{i=1}^{a}(a-i+1)^(a-i+1)

Homework Helper
hi oscaralive!

(try using the X2 icon just above the Reply box )

isn't that just 11223344…aa

why not leave it as it is?

(or you could write it as (a!)a over something)

oscaralive
Because i'm trying to find an upper bound to define the complexity of an algorithm....and I cannot put it that way...it would be great to find an appropriate upper bound to this product

Thanks

Homework Helper
well, the log would be ∑nlogn … does that help?

oscaralive
In fact, I come from the log serie...

$$\sum_{i=1}^{a}(a-i+1)log(a-i+1)$$

$$\sum_{i=1}^{a}log((a-i+1)^{(a-i+1)})$$

$$log(\prod_{i=1}^{a}{(a-i+1)}^{(a-i+1)})$$
which now has been transformed to the product...

thanks,

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