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16h
awarded  Constituent
Dec
15
awarded  Caucus
Dec
12
comment Simpler way to evaluate the Fourier transform of $\exp\left(i e^x\right)$?
How do you know that you can break the integral up in two parts, that is to say how can you conclude from the divergence of the individual parts that the original integral did diverge?
Nov
23
comment First order ODE: $y'=\frac{b\sqrt{x^2+y^2}-ay}{ax}$
the integral is far from easy but then maybe you should add to your question what you have done and present the integral such that people can help you with that...
Nov
23
comment First order ODE: $y'=\frac{b\sqrt{x^2+y^2}-ay}{ax}$
As you already know the "correct" substitution you should go ahead and solve the resulting equation for $u(x)$ via separation of the variables.
Nov
21
comment How can I write in Landau notation (or the like) that $2^x/x$ rises almost as fast as $2^x$?
@ErickWong: no it doesn't.
Nov
21
comment How can I write in Landau notation (or the like) that $2^x/x$ rises almost as fast as $2^x$?
@DaveBallakauser750378: why $\log 2^x= x \log2$ is not in $O(\log(2^x/x)) = O(x \log 2 + \log x)$?
Nov
21
comment Using Fourier analysis to show a function is positive
+1 Just for reference: this is also called Poisson summation formula.
Nov
21
comment How can I write in Landau notation (or the like) that $2^x/x$ rises almost as fast as $2^x$?
How about taking the logarithm and writing $\log(2^x/x) = O(\log 2^x)$?
Nov
19
comment Integral of Bessel function with Gaussian over a quadratic
@TomBolton: so the answer is simply infinity as there is a divergence for $x= c^{-1/2}$.
Nov
19
comment Integral of Bessel function with Gaussian over a quadratic
@TomBolton: the constants seem to be important as for $c>0$ the integral simply diverges. It also diverges for all $\text{Re} \,b <0$. So unless you tell us where in the complex plane your parameters are it will be hard to help you.
Nov
19
revised Integral of Bessel function with Gaussian over a quadratic
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Nov
19
comment Integral of Bessel function with Gaussian over a quadratic
You see from @RonGordon's answer that for $c>0$ it is easy to "evaluate" the integral. It might be good if you could provide some context (where does this problem come from) and tell us what values you want the parameters $a,b,c$ to obtain.
Nov
7
awarded  Revival
Nov
5
answered calculate $\int_\gamma \frac{dz}{z}$ using $\ln(z)$ function
Oct
20
comment Why is there two versions of the rotation matrix?
There is the additional complication that one can define active and passive transformations (which is always confusing for people).
Oct
11
revised Efficient software implementation of $x^2+3y^2=N$
added 539 characters in body
Oct
11
revised Efficient software implementation of $x^2+3y^2=N$
deleted 16 characters in body
Oct
11
answered Efficient software implementation of $x^2+3y^2=N$
Sep
30
awarded  Explainer