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Oct 1	comment	Cauchy's residue theorem with an infinite number of poles Sorry, I was thinking of a contour, say some hemisphere, whose radius goes to infinity (oriented appropriately), and I was just thinking of isolated singularities within the contour. Talk of non-isolated singularities just threw me a bit.
Oct 1	comment	Cauchy's residue theorem with an infinite number of poles so if there are a countable number of isolated singularities within the contour, say at the positive integers only, then we can apply the residue theorem so long as the infinite sum of their residues converges?
Oct 1	comment	Cauchy's residue theorem with an infinite number of poles but what if the integrand has infinitely many singularities at the positive integers only, for example. Each of these singularities is isolated, but there are just infinitely many of them. None of these are non-isolated singularities.
Sep 30	revised	Cauchy's residue theorem with an infinite number of poles deleted 1 characters in body
Sep 30	asked	Cauchy's residue theorem with an infinite number of poles
Sep 26	comment	How to find the derivate of the function $f(x)=x^{x^{x}}$ Is $f(x)=x^{(x^x)}$ or $f(x)=(x^x)^x$?
Sep 25	accepted	Proving two expressions can never be simultaneously satisfied
Sep 25	comment	Proving two expressions can never be simultaneously satisfied This is very insightful, thanks. Is there a typo here... should we not have $\sum a_i^2=0$.
Sep 25	revised	Proving two expressions can never be simultaneously satisfied added 43 characters in body
Sep 25	comment	Proving two expressions can never be simultaneously satisfied No this is not my question. My first question asks whether my approach to the example problem is correct. My second question asks if anyone knows of any general tools or theories which might be of use to attack such problems. For example, for $f$ and $g$ linear I am aware we can frame the question as a simultaneous equation and solve that way.
Sep 25	asked	Proving two expressions can never be simultaneously satisfied
Sep 21	awarded	Custodian
Sep 21	accepted	Functions of a complex variable and the Cauchy-Riemann equations
Sep 20	asked	Functions of a complex variable and the Cauchy-Riemann equations
Sep 14	accepted	Is the Glaisher–Kinkelin constant transcendental?
Aug 31	comment	Is it possible to express $e$ in terms of $\pi$ algebraically and vice-versa? Yes, but what you are saying above is that $e=e^{i(−1/\pi)i\pi}$, so in fact you're expressing $e$ in terms of $e$ and $\pi$, not $\pi$ alone.
Aug 31	comment	Is it possible to express $e$ in terms of $\pi$ algebraically and vice-versa? @Gary Myerson I don't think so since then we would have $$e=(-1)^{i(-1/\pi)}=e^{i(-1/\pi)\log(-1)}=e^{i(-1/\pi)i\pi}=e,$$ so we just get back what we started with.
Aug 30	accepted	Is it possible to express $e$ in terms of $\pi$ algebraically and vice-versa?
Aug 30	comment	Is it possible to express $e$ in terms of $\pi$ algebraically and vice-versa? So there could be an algebraic relation that exists that we just don't know of. Ok.
Aug 30	comment	Is it possible to express $e$ in terms of $\pi$ algebraically and vice-versa? But doesn't $e^{i\pi}+1=0$ show them to be algebraically independent?