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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.


Jun
7
answered A pyramid has a square base with sides of length 4. If the sides of the pyramid are equilateral triangles, what is the pyramid's volume?
Jun
5
revised $\sum_{k=1}^{\infty} \frac{a_1 a_2 \cdots a_{k-1}}{(x+a_1) \cdots (x+a_k)}$
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Jun
5
revised $\sum_{k=1}^{\infty} \frac{a_1 a_2 \cdots a_{k-1}}{(x+a_1) \cdots (x+a_k)}$
deleted 163 characters in body
Jun
5
answered $\sum_{k=1}^{\infty} \frac{a_1 a_2 \cdots a_{k-1}}{(x+a_1) \cdots (x+a_k)}$
May
30
revised Is $y'=1+y^n$ periodic function for $n>2$?
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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
revised Is $y'=1+y^n$ periodic function for $n>2$?
edited title
May
30
revised Is $y'=1+y^n$ periodic function for $n>2$?
edited body
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
30
asked Is $y'=1+y^n$ periodic function for $n>2$?
May
29
accepted To evaluate $\int_0^{+\infty} \frac{\;dx}{\sqrt[3]{x^3+a^3}\sqrt[3]{x^3+b^3}\sqrt[3]{x^3+c^3}}$
May
22
revised How to find the curve equation
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May
22
asked How to find the curve equation
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
15
accepted Can we prove that all equations can be solved via complex numbers?
May
14
awarded  Popular Question
May
13
answered Prove that $\lim_{n\rightarrow\infty} \frac{1}{n}\sum_{k = 1}^{n}{f(\frac{k}{n}) }$ $=\int_0^1 f(x)dx.$
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.