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Feb
7
answered Prove $\left(1+\frac{x}{n}\right)^n < e^x$, where $x$ is any positive real number and $n$ is any positive integer.
Feb
7
comment On a “coincidence” of two sequences involving $a_n = {_2F_1}\left(\tfrac{1}{2},-n;\tfrac{3}{2};\tfrac{1}{2}\right)$
Do you have a background about special functions?
Feb
7
comment Fourier coefficients of the Gaussian.
Here is a useful integral for you
Feb
7
comment Fourier coefficients of the Gaussian.
You are very welcome! By the way where did this problem come from?
Feb
7
comment Area of a rectangle within a curve
You are asked to find the shaded area of the cross section!
Feb
7
comment Fourier coefficients of the Gaussian.
The integral is not elementary! You can have an answer in terms of the error function. See [here] (m.wolframalpha.com/input/…).
Feb
7
comment Fourier coefficients of the Gaussian.
Have you tried mathematica or maple?
Feb
7
comment Convolution $f * g$
@AbdouAbdou: thank you! I really appreciate it.
Feb
7
revised Convolution $f * g$
deleted 1 character in body
Feb
7
comment Solve the equation $\Bbb|x-\sqrt{x}|=\lfloor x\rfloor-\sqrt{x}$
$x=0,1,2,3,\dots $ is a possible set of solutions.
Feb
7
comment Why is continuity needed to substitute value of derivative inside Riemann-Stieltjes Integral?
It says f is increasing!
Feb
7
revised Convolution $f * g$
Adding more material
Feb
7
answered Convolution $f * g$
Feb
7
comment Convolution $f * g$
Just write down the integral which represents the convolution of the two functions!!
Feb
7
comment Estimate $|f(x)| \le \frac C{|x|^3}$
Are you sure it is $\frac{C} {|x|^3}$ not $\frac{C} {|x|}$?
Feb
6
comment How to find branch points for complex functions?
Do you know the definition of a branch point? What have you been taught about it?
Feb
6
comment limit of $\frac{(k+1)[x^k(a+sin(x^{-k-1}))-x^{-1}cos(x^{-k-1})]}{k[x^{k-1}(a+sin(x^{-k}))-x^{-1}cos(x^{-k})]}$ as $x \to 0$
limit does not exist.
Feb
6
comment Is there a nice closed form to $\int_0^{\pi/2} (\log \sin x)^n\text{ d}x$ for $n\in \Bbb{Q},n\gt 1$?
@Lucian: thank you! I appreciate it.
Feb
6
answered Is there a nice closed form to $\int_0^{\pi/2} (\log \sin x)^n\text{ d}x$ for $n\in \Bbb{Q},n\gt 1$?
Feb
5
comment Why does the solution of $y'' = -(1+e^x)y$ decay like $e^{-x/4}$?
@JyrkiLahtonen : why my comment was deleted?