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1d
answered Show that if $X$ may be deformed into $Z$ then $X$ and $Z$ are cobordant.
1d
comment Nested Sum Encountered in Maclaurin Expansion of $e^{-x^2}$
almagest, your reformulation inspired me and I finally figured it out! See the answer I posted if you want to see the nitty-gritty details. Thanks!
1d
answered Nested Sum Encountered in Maclaurin Expansion of $e^{-x^2}$
Sep
17
awarded  Supporter
Sep
17
comment Necessary and Sufficient Conditions for $f_{xy} = f_{yx}$
You are correct. I misinterpreted what you were attempting to say. However, this is a simple restatement of the original theorem. In a sense, I'm asking that if we declare the mixed partials to be equal, then what can we deduce about $f$? Also, see my original post, edited to ask about some relevant illustrative examples.
Sep
17
revised Necessary and Sufficient Conditions for $f_{xy} = f_{yx}$
added 306 characters in body
Sep
17
comment Necessary and Sufficient Conditions for $f_{xy} = f_{yx}$
The construction of $f$ there is clever. Thank you.
Sep
17
comment Necessary and Sufficient Conditions for $f_{xy} = f_{yx}$
@Graham, nice formatting. However, the "change of order" step is only valid assuming continuity of second partials. You accidentally included a bit of your conclusion in your premise.
Sep
17
revised Necessary and Sufficient Conditions for $f_{xy} = f_{yx}$
edited title
Sep
17
asked Necessary and Sufficient Conditions for $f_{xy} = f_{yx}$
Sep
5
comment Calculating limits of functions explicitly
@Nir, Check my edits to see if it addresses your question. Remember x*y = y/(1/x) (except when x=0), so with limits you can often use this trick to get things in a form where L'Hopital's Rule applies.
Sep
5
revised Calculating limits of functions explicitly
Updated to a more explicit example
Sep
4
awarded  Yearling
Sep
3
awarded  Editor
Sep
3
revised Nested Sum Encountered in Maclaurin Expansion of $e^{-x^2}$
deleted 16 characters in body
Sep
3
comment Nested Sum Encountered in Maclaurin Expansion of $e^{-x^2}$
Thank you. The recursive definition you reformulated the sum into is quite nice. I don't, however, see the 'easy induction' proof. Would you mind suppressing the laziness urge providing a little more in the way of proof? :) Also edited question to more clearly state desire of proof.
Sep
3
answered Calculating limits of functions explicitly
Sep
3
awarded  Student
Sep
3
comment Nested Sum Encountered in Maclaurin Expansion of $e^{-x^2}$
@user166967, they are just indices of the respective sums.
Sep
3
asked Nested Sum Encountered in Maclaurin Expansion of $e^{-x^2}$