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April 25

Generalization of l'Hôpital's rule to functions of more than one variable

This rule is very useful when finding otherwise-indeterminate forms, but the article on it only defines the rule for a function of a single independent variable. But suppose I want to find a multi-variate indeterminate form - e.g., the ratio of two multivariate functions of the same set of variables that both tend to zero or infinity as the independent variables are allowed to approach a specific point. Is there a generalization of this rule that allows it to be used for such limits?--Jasper Deng (talk) 06:22, 25 April 2013 (UTC)[reply]

This seems quite a common question have a look at stack exchange. The general answer seems to be no, as the limit can change depending on which path you take although there may be cases where it be made to work.--Salix (talk): 07:36, 25 April 2013 (UTC)[reply]

What did Hilbert have to do with the Hilbert–Pólya conjecture?

Our article on the Hilbert–Pólya conjecture says it was thought up in 1982 by George Pólya. If it says anywhere what it has to do with Hilbert, I'm missing it. Can anyone elucidate (and, if possible, amend the article)? Marnanel (talk) 08:57, 25 April 2013 (UTC)[reply]

It's all a bit vague, but see http://www.dtc.umn.edu/~odlyzko/polya/index.html, which is referenced in our article. Looie496 (talk) 16:31, 25 April 2013 (UTC)[reply]