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seen Aug 23 at 7:31

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.


Jul
3
accepted The volume and surface area of pipe?
Jul
2
answered Show $\lim_{N\to \infty}\sum_{k=1}^{N}\frac{1}{k+N}=\ln(2)$
Jul
2
awarded  Nice Answer
Jul
2
comment Number of distinct $f(x_1,x_2,x_3,\ldots,x_n)$ under permutation of the input
Thanks a lot for your answer. Could you please give more detail how you got the general formula $\tbinom{n}{n/2}/2$ for n is even? I wonder why a general formula cannot be found for all n. It is strange that odd zeta function values do not have closed form expression of $\pi$ too such as $\zeta(3),\zeta(5) etc$. I started to suspect a relation between them?????*. And Also there should be proofs of Abel-Ruffini that don't use group theory because Historically Abel-Ruffini offered their ideas before grup theory of Galois . Thanks a lot for your valuable response.
Jun
30
accepted To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
Jun
29
comment The volume and surface area of pipe?
:Thanks a lot for detailed edit.
Jun
28
revised Number of distinct $f(x_1,x_2,x_3,\ldots,x_n)$ under permutation of the input
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Jun
28
revised Number of distinct $f(x_1,x_2,x_3,\ldots,x_n)$ under permutation of the input
deleted 43 characters in body
Jun
28
revised Number of distinct $f(x_1,x_2,x_3,\ldots,x_n)$ under permutation of the input
added 1810 characters in body
Jun
28
comment The volume and surface area of pipe?
Thanks a lot for answer. What about overlap status? Are the formulas still correct? if no, what to do in this case?
Jun
28
comment To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
@Sasha Thanks a lot for your help. very much appreciated
Jun
28
comment To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
Thank you very much for very detailed steps. I got many nice point. Now I wonder how can $u_{\alpha}(x)$ be expressed as series? For your information: There is no any context at least I do not know. I would like to know as well if any context that includes that function. Maybe someone else can refer. The question is my own interest and searching result. I am interested in second order differential equations and looking for different ways to find general solution of those. Thanks a lot for your answer again .
Jun
27
comment To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
Wolfram Alpha gave long solution with hyper-geometric functions too .wolframalpha.com/input/?i=x+u%27%27+%2B%28x-a%29u%3D1 . looks very easy differential equation but result is not. I need to find different approach to find closed form of U. Thanks for all kind of advice.
Jun
27
comment To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
Wawww. This output looks very complex. What about hypergeometric function expressions for that diff equation. After some transforms is it possible to get more simple way. thanks for advice
Jun
27
comment To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
Could you please help to find the solution of differential equation too? Thanks a lot for answers
Jun
27
revised To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
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Jun
27
accepted To simplify $f_a(x)= \int_{-a}^{+a} e^ {-\frac{x}{t^2-a^2}}\;dt$
Jun
27
asked To find closed form of $\int_0^{\frac{\pi}{2}} e^{-x\tan t+\alpha t} \;dt $
Jun
27
revised Proving the identity $\sum\limits_{k=1}^n {k^3} = {\Large(}\sum\limits_{k=1}^n k{\Large)}^2$ without induction
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Jun
27
answered Proving the identity $\sum\limits_{k=1}^n {k^3} = {\Large(}\sum\limits_{k=1}^n k{\Large)}^2$ without induction