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# Symbolic product in Sage?

Suppose I'd like to compute

prod(1/x^4, x, 1, oo)


How can this be done?

I found an old thread, but with no answers.

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## 4 Answers

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Take the natural logarithm of your product and you get a sum which can be evaluated:

$$\ln\left( \prod_{x=1}^k \frac{1}{x^4} \right) = \sum_{x=1}^k \ln\left(\frac{1}{x^4}\right)$$

... now take the limit as $k \to \infty$:

sage: sum(ln(1/x^4), x, 1, oo)
-Infinity
sage: e^sum(ln(1/x^4), x, 1, oo)
0

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In Sage, sum serves both for Python sums and for symbolic sums, but for products we have prod and product.

sage: product(1/x^4, x, 1, oo)
0


This should be better documented... See

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I have the same problem. If someone know how to do

more I found symbolic sum but not symbolic product in the reference files. I need to be able to classify a function of a erratic x which involve several symbolic foodstuffs from 1 to n or whatever. I then want to be able to do a derivative and a limit of this. I am trying out Sage because Mathematical doesn't seem to be able to handle this stuff exactly. I can define the function just fine but when I try to take the limit Mathematical can't seem to handle it.

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Asked: 2012-06-08 14:13:32 +0200

Seen: 1,611 times

Last updated: Apr 16 '20