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I am an engineer who is in love with math and lifelong math student. I love to learn new things in mathematics for self-satisfaction. My idols are Gauss , Euler , Ramanujan because they were in love with math as I feel.


Aug
14
comment How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
@Winther Thanks a lot for comments. The final expression is very beautiful. I will focus on some examples to confirm .It can be used as a nice tool.
Aug
14
comment How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
@ChristianBlatter $$ f(x)+\frac{y.f''(x)}{2!}+\frac{y^2 f^{(4)}(x)}{4!}+\cdots=\frac{1}{2} (e^{\sqrt{y}S}(f(x))+e^{-\sqrt{y}S}(f(x)))=\frac{1}{2}(f(x+\sqrt{y})+f(x-\sqrt{y‌​}))$$ but I am looking for a closed form of $ f(x)+\frac{y.f''(x)}{1!}+\frac{y^2 f^{(4)}(x)}{2!}+\cdots$ if we can express it as $\sum a_n(y)f(x+b_n(y))$ or not
Aug
14
comment How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
@Winther I updated as you commented. Is it correct what I got? It seems The form is an integral transform of that operator but no any relation for a linear f formula. Maybe I need to do some more transforms in last integral to get my aim. Thanks for advice
Aug
14
comment How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
@Winther Could you please check my last edit? I believe it can help to prove or disprove that a linear in f-formula exists or not. Thanks for help.
Aug
6
comment Remove unlogical points (noise) in a curve
@tknew the second link shows in examples how it works . If It looks ok to use for your purpose , you may try the library. I think first one finds only one strange value but you need to define more. Maybe you can run three times the function to find your three strange value via using first link library. Really this depends on you. Mostly filters have been used for signals that flows in real time. This kind of real time signals can have any time noise and we cannot estimate how many input affected.
Aug
5
comment Is there any proof for this simple observation?
I recommend you read the paper "Geometry for N-Dimensional Graphics" cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/ggndgeom.pdf
Aug
1
comment To find the center of gravity of a homogeneous tetrahedron
@anderstood : homogeneous means there is a material inside it and distributed equally in each point of tetrahedron .
Jul
31
comment To find the center of gravity of a homogeneous tetrahedron
What about triangle formula if we think in your way? Is it wrong ? Please think that we have $P_1,P_2,P_3$ and if $P_1=P_2$ then the formala $O(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})$ cannot be true for the center coordinate of homogenous triangle but it is true.
Jul
21
comment To find the volume of the region that is bordered by 4 points in 3D space
I tested the formula on a simple 4 points examples such as $(0,0,0),(1,0,0),(0,1,0),(0,0,1)$ that $V=1/6$.It should be factorial factor as you said for $3D$. I missed that point but I wonder how to prove that it is true for higher dimensions. We cannot figure out in mind the higher dimensions than 3D,can we? How did they prove that? Do you know a related links or reference books for that subject? Thanks a lot for your help.
Jun
10
comment To find a fifth degree equation by using circles and lines that cannot be solved by radicals
@mercio : I am aware that circles and lines is solvable by square roots, I wonder if we try to find angles (trigonometric equations. Please see my previous question). Thanks
May
30
comment Is $y'=1+y^n$ periodic function for $n>2$?
@vadim123 The inverse function can be expressed as $a_1\ln(y-y_1)+a_2\ln(y-y_2)+...+a_n\ln(y-y_n)=x+c$ and then $(y-y_1)^{a_{1}}(y-y_2)^{a_{2}}...(y-y_n)^{a_{n}}=Ke^{x}$ . I think that way but I do not know how to go forward to prove they are periodic like $tan(x)$.Thanks
May
30
comment Is $y'=1+y^n$ periodic function for $n>2$?
@lhf Please check for $n=2$ , same kind of graph it draws.wolframalpha.com/input/?i=y%27%3D1%2By%5E2
May
21
comment Easiest way to prove integral of $e^{ikx}$ is $\delta(k)$
Please see other answer .As i wrote, Priyatham's answer gave that proof
May
21
comment Easiest way to prove integral of $e^{ikx}$ is $\delta(k)$
: It is just a defination : You could say $\lim\limits_{ a\to \infty } f_a(x) = \lim\limits_{ a\to \infty } 2\frac{\sin {ax}}{x}= g(x)$ and you could try to draw $g(x)$. You can see some $a$ values how affect the graphs. You will get $g(x)$ as impulse graph if $a--->\infty$ . Then If you use Priyatham result in other question, you could see that For $\epsilon>0$ $$ \int\limits_{-\epsilon}^\epsilon g(x) \mathrm{d}x = 2\pi$$ Finally Somebody defined that $g(x)=2\pi \delta(x)$. Is it ok now proof?
May
21
comment Easiest way to prove integral of $e^{ikx}$ is $\delta(k)$
Please check this math.stackexchange.com/questions/558077/…
May
9
comment Can we prove that all equations can be solved via complex numbers?
@5xum Thanks a lot for you answer. You gave good point and link to see which theorem related to my question but I really need to understand the proof. Maybe someone can help me with elementary proof.
May
5
comment Can we prove that all equations can be solved via complex numbers?
@user99680 erf(z) is an just example that equation can be very hard to see solution. I could write much more longer , I want to see general proof for analytic function equations .
May
5
comment Can we prove that all equations can be solved via complex numbers?
if we do not use $\bar z$???. I mention we will use just analytic functions.
Apr
26
comment Infinite series representation of elliptic integrals $F(k,\phi)$ and $E(k,\phi).$
Did you check wiki page ? The same result you got for K(k) series expansion en.wikipedia.org/wiki/Elliptic_integral
Apr
17
comment What is the integral $\int x^t/\Gamma(1+t) \, dt$? (In general: relation between series and integrals)
See the question .it is related:math.stackexchange.com/questions/158527/…