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 Jul5 comment Evaluating $\int\limits_{-\infty}^\infty {\exp(iax)\over1+ix}dx$ This looks like the Fourier Transform. Jun30 comment How to find the eccentricity of this conic? What level are you asking this question from,... is this a pre-calculus course? Just so the responses and terminology would be more appropriate for your level. If so, you might want to tag your question with pre-calculus or the related as well. Jun30 comment Laplace transform of $1/t$ Or more simply: $t^n \stackrel{\mathcal{L}}{\Longleftrightarrow} \frac{n!}{s^{n+1}}$ without involving the gamma ($\:\Gamma\:$) function. Jun28 comment Evaluation of these integrals @draks: Of course not :D, using a CAS. Is it possible to get polylog function by hand or recognize it from doing intergrals? I just thought this was a CAS algorithmic way of deducing the problem into a more complex answer using special functions, because an elementary table look up failed. So it resorted to special solution techniques. Although $\tan k$ is considered a simple function but not sure about hyperbolic tangent :) Jun28 comment Evaluation of these integrals I get this for integral one: Not sure if equivalent to Norbet answers. $\int_0^p \! ktanh(\pi k)=-(1/24)(-\pi^2+12p^2\pi^2-24p\ln(1+exp(2p\pi))\pi-12polylog(2,-exp(2p\pi)))/(‌​\pi^2)$ Jun28 comment Solving a complex integral Similar type of question from a $\mathbb{R}$ domain standpoint. math.stackexchange.com/questions/73250/… Jun28 comment Fundamental solution of the wave operator Have a look here for starts: math.ucsd.edu/~lindblad/110b/l17.pdf math.ucsd.edu/~lindblad/110b/l18.pdf Apr29 comment Definition of Sinc function Very nice answer. :) Apr19 comment Definition of Sinc function @J.M.: I guess it was really not needed to state both. I could of just stated the one of preference (or of matter here). But I just included for others who may be only familiar with one definition over the other. Apr19 comment Definition of Sinc function @J.M.: Please see here: en.wikipedia.org/wiki/Sinc_function Apr19 comment Definition of Sinc function @J.M.: What do you mean by using one name for two different functions? I'm more so used to the normalized form. Mar25 comment Integral Transform @Mathlover: where does the $e^t$ go, that's on the outside of the integral on the RHS of the equation? Mar24 comment Integral Transform @Tpofofn: Thanks, I realized that. But I need the function $w(t)$ to determine the output to another system with $w(t)$ being the input. This is why I needed to integrate or use properties to transform $W(f) \leftrightarrow w(t)$. Mar23 comment Integral Transform @Mathlover: Ah hah, I knew that integral looked familiar. I do not have a book handy, but is this a transform pair I believe or property? I just remember seeing it sometime ago, but haven't used it before. Which now makes more sense in terms of what functional constructs that has infinite amplitude, such as the dirac. Thank You! Mar23 comment Integral Transform @Mathlover: I didn't get what you meant by that. It would be in terms of $f$ correct because its indefinite and its whats the independent variable is for that case, right? So would our $w(t) = e^t\int_{-\infty}^{\infty} j\pi f e^{j2\pi ft} df$? Mar23 comment Integral Transform @Mathlover: Exactly is what I get. I had done: $\frac{d}{dt}(w(t)e^t)=\frac{d}{dt}(\int \! \frac{j\pi f}{1+j2\pi f}e^{(j2\pi f+1)t} df)=\frac{e^{t+2 i \pi f t} (2 \pi f t+i)}{4 \pi t^2}$, because I know the integral would not converge, but when doing: $\frac{d}{dt}(w(t)e^t)=\frac{d}{dt}(\int_{-\infty}^{\infty} \! \frac{j\pi f}{1+j2\pi f}e^{(j2\pi f+1)t} df)$, it equal to what you have. So, for this last integral equation, this would be what $w(t)$ is? That's pretty interesting, for it to be in terms of a definite integral. Mar23 comment Integral Transform @Mathlover: Thanks. So when doing this, I get for the right hand side before evaluating the limits is: $\frac{e^{t+2 i \pi f t} (2 \pi f t+i)}{4 \pi t^2}$. Now, plugging in limits, the integral will not converge on $[-\infty,\infty]\,$. How do we go from here to fully obtain the inverse of $W(f)$? Mar23 comment Integral Transform @Tpofofn: Thanks, I just realized I did not need to find the inverse to get $w_1(t)$ because it was only asking for the frequency spectrum. But, how would I find the inverse of $W(f)$ to get what $w(t)$ is. Either using the definition which I started, or transform properties. I managed to get this from using the properties but not sure if it is correct: $w(t)= 1/2e^{-t}\frac{\mathrm{d}w}{\mathrm{d}t} u(t)\,$ where $u(t)$ is the unit step function. Feb27 comment Nice proofs of $\zeta(4) = \pi^4/90$? I wondering what does the $\zeta$ represent? Is that of any significance or just a variable? Feb18 comment Sifting out Solutions to Differential Equations Hey Julian, This is a really well thought out response and helpful to know for future reference and work/research. Thank You.