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 Feb 19 comment What is known about the complex solutions to $\zeta(s)=-1$? My thoughts too. I was just wondering if there was anything in the literature on this "other case". Are there multiple solutions or just one solution, etc. For example, in the case $\zeta(s)=0$ it is known that there are an infinite number of such $s$ on the critical line. NB I've changed the title to reflect what I'm trying to get at. Feb 19 asked What is known about the complex solutions to $\zeta(s)=-1$? Feb 16 revised Can a substitution cause a convergent definite integral to diverge? added 364 characters in body Feb 11 comment How do you define the derivative of a function without an argument? Maybe Differential Fields, with the operator $D$ is what you're looking for. Feb 4 comment Proof of the limit using only elementary techniques @TonyK ok yes not a limit ("tends to") - my mistake. But maybe it is approximately $e^n$. Feb 4 comment Proof of the limit using only elementary techniques Does this imply $\text{lcm}(1,2,\ldots,n)\to e^n$ as $n\to\infty$ ? Feb 4 revised Complex integration identity added 1 character in body Feb 2 comment Examples of double surface integrals I found these online tutorials to be very good: tutorial.math.lamar.edu/Classes/CalcIII/… Feb 2 revised Find a value for a number to the power of a complex number added 1 character in body Jan 31 revised Trigonometric integral (arctg) added 13 characters in body Jan 24 revised The meaning of dot centered vertically, as in $3\cdot 5$ added 12 characters in body Jan 24 answered The meaning of dot centered vertically, as in $3\cdot 5$ Jan 22 awarded Yearling Jan 21 comment Logarithms of Negative Numbers $\log z=\log|z|+i\text {Arg} z$ if you take the principal branch. Exponentiating both sides gives $z=|z|e^{i\text{Arg}( z)}$ as you might hope to expect. Jan 20 comment Computing the integral of $\int \frac{25x^2}{(x+3)(x-2)^2}\,dx$ what is "impartial differentiation" ? Jan 20 comment Proof of $\cos(y)$ and $\sin(y)$ using $e^{iy}$ A simple case of substitution followed by simplification will achieve what you want. Jan 20 revised Solving $x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y }=1$ deleted 19 characters in body Jan 20 comment Does $\int_0^\infty \sin(x^{2/3}) dx$ converges? Maybe $$I=\Im\int_0^\infty e^{ix^{2/3}}dx,$$ and then use the error function. Looks divergent. Jan 20 revised Closed form for $\prod_{k=1}^n (a+k^2)$ edited body Jan 20 revised Closed form for $\prod_{k=1}^n (a+k^2)$ deleted 2 characters in body