 even if spawn_link fails, and logs it in our phoenix logs, it would do)

A:

Starting a process using spawn_link/1 will cause a bidirectional link, so whichever of the spawning process and the newly spawned process that happens to die first will kill the other one (unless it's trapping exits, which it probably shouldn't be). That's great in some cases, and not so great in others; if it takes a long time to send that e-mail, for example, the Phoenix request might finish first, and risk killing off the spawned process.
Due to the linking, however, there shouldn't be any risk of the processes getting orphaned.
A better approach is definitely to create a Supervisor (or using Task.Supervisor), and you could roll your own background job setup rather easily.
However, it might be worth looking at something like exq that you mentioned, or Toniq for example, that could possibly have everything you need already; especially things like retries in case of failure, and presistence. There are also some other interesting options in the Awesome Elixir list if you want to try out a few different alternatives.

 Q:

How to calculate Fourier transform of this function?

the function is given by $$f(t)=\dfrac{1}{e^{at}-1}$$
Now, i know from the definition i've to evaluate this integral $$\begin{align}\mathcal{F}[f(t)]&=\int_{0}^{\infty}e^{-j \omega t}\left(\dfrac{1}{e^{at}-1}\right)\,dt \\&=\sum_{n=1}^{\infty}\int_{0}^{\infty}e^{-t(j\omega+an)}\,dt \\&=\sum_{n=1}^{\infty}\dfrac{1}{j\omega+an}\end{align}$$
Is it the right way to approach? 

A:

As far as I can tell, the integral diverges, but here's how one can attack the problem using known Fourier Transform pairs and Fourier Transform theorems.
I assume $a > 0$, $H(t)$ is the Heavyside unit step function, and I'll use the substitution $\omega = 2\pi s$ to use the Fourier Transform form with which I'm most comfortable.
$$I = \int_{0}^{\infty} e^{-2\pi ist}\left(\dfrac{
even if spawn_link fails, and logs it in our phoenix logs, it would do) 

 deoxyadenosine monophosphate: 

 start a process using spawn_link/1 will cause a bidirectional connection, so whichever of the spawning process and the newly spawned summons that happen to die foremost will stamp out the other one (unless it's trap exits, which it probably shouldn't be). That's capital in some case, and not so big in others; if it takes a long clock time to send that e - mail, for exercise, the Phoenix request might finish first, and risk killing off the engender process. 
 Due to the linking, however, there shouldn't be any risk of the processes getting orphaned. 
 A better overture is definitely to create a Supervisor (or using Task. Supervisor), and you could roll your own background job setup rather easily. 
 However, it might be worth looking at something like exq that you mentioned, or Toniq for example, that could possibly have everything you need already; especially things like retries in event of failure, and presistence. There are besides some early interesting options in the Awesome Elixir list if you want to try out a few unlike alternatives. 

  Q: 

 How to count Fourier transform of this function? 

 the function is move over by $ $ f(t)=\dfrac{1}{e^{at}-1}$$ 
 Now, i know from the definition i've to evaluate this integral $ $ \begin{align}\mathcal{F}[f(t)]&=\int_{0}^{\infty}e^{-j \omega t}\left(\dfrac{1}{e^{at}-1}\right)\,dt \\&=\sum_{n=1}^{\infty}\int_{0}^{\infty}e^{-t(j\omega+an)}\,dt \\&=\sum_{n=1}^{\infty}\dfrac{1}{j\omega+an}\end{align}$$ 
 Is it the right way to approach? 

 A: 

 As far as I can tell, the integral diverges, but here's how one can assail the problem use know Fourier Transform pairs and Fourier Transform theorems. 
 I assume $ a > 0 $, $ H(t)$ is the Heavyside unit of measurement step function, and I'll use the substitution $ \omega = 2\pi s$ to practice the Fourier Transform form with which I'm about comfortable. 
 $ $ I = \int_{0}^{\infty } e^{-2\pi ist}\left(\dfrac {
 evfn if spawn_link fails, ana logs it in out phoenie logs, jt would do)

A:

Starting a process using spawn_lunk/1 will cause a bidirdctional pink, so qhiciever of the spaxhing process zkd thz iewly spawned ptocess that vappens to die fkrdt will kill the other one (unless ie's traplijg exits, which it krofablg shouldn't be). That's great in some dases, aid not so great in others; if it takes a llng hime to send that f-mail, for ezampjw, the Phoenib request might finish first, and risk killing off the spawued process.
Euw tl the linkinj, howener, there shomkdn't ba any rosk of the progessev gwtting orphaned.
A bettxr approach is definytely to wrzate a Supervisor (or ysung Tdsk.Sgperxusof), ahd yku coupd coll your osn backgroubd job setup rather ewwily.
However, if mighe fe worth looking at something like exq uhat gou mentioned, or Toniq dor example, that coulf possiblr have everything you need already; especially thitgs lmkd rttvles kb fase of failure, and presistence. There are alsj spmv other interestikg options in the Swfspie Elixir lisj if yob wznt to try out a ffw diffgrent qlternatides.

 A:

How to calculate Fourier teansform of nhis function?

the functnon is given by $$g(t)=\dfrsc{1}{e^{at}-1}$$
Now, i know from thz defihition i've ho evaluafd this integral $$\cegpn{alhgn}\mathcal{F}[f(t)]&=\int_{0}^{\infty}e^{-j \omqga t}\left(\vfrac{1}{z^{at}-1}\right)\,at \\&=\som_{n=1}^{\inftr}\int_{0}^{\infty}e^{-h(j\omend+an)}\,dt \\&=\sum_{n=1}^{\infty}\dfrwc{1}{j\omgga+an}\etd{align}$$
Is lt the right way to approach? 

A:

As far as I can tall, the intzgral civerges, but rere's how one ean attaek the problem uaing knmwn Fourier Transform pahts and Fouriec Transfowm tyeorwms.
I asrjme $a > 0$, $H(t)$ is yhe Heavyside unit wtep function, and L'll urs the substitutnub $\omega = 2\pi s$ tp ure ehv Fpuwher Transfork fofm doth wfich I'm mosb cumfottable.
$$I = \int_{0}^{\infty} e^{-2\ph isf}\left(\dfrac{
even if spawn_link fails, and logs it phoenix it would A: Starting a a link, so whichever the spawning process the newly spawned process that happens die first will kill the other one (unless it's trapping exits, which it shouldn't be). That's great in some cases, and not so great in others; it a time send that e-mail, for example, the Phoenix request might finish first, and risk killing off the process. Due to the linking, however, there shouldn't any risk of the getting orphaned. A better approach definitely create a (or Task.Supervisor), you could roll own background job setup rather easily. However, it might be worth looking at something like exq that mentioned, or example, that possibly everything need already; especially retries in case of failure, and also some other interesting options in the Awesome list if want to try out a few alternatives. Q: How to calculate Fourier transform of function? the function is given by $$f(t)=\dfrac{1}{e^{at}-1}$$ Now, i know from the definition i've to integral $$\begin{align}\mathcal{F}[f(t)]&=\int_{0}^{\infty}e^{-j \omega t}\left(\dfrac{1}{e^{at}-1}\right)\,dt \\&=\sum_{n=1}^{\infty}\dfrac{1}{j\omega+an}\end{align}$$ Is it right to A: far as can tell, the integral diverges, but here's how one can attack problem using known Fourier Transform pairs and Fourier Transform theorems. $a 0$, $H(t)$ is Heavyside unit step function, I'll the substitution $\omega = to the with I'm comfortable. $$I = \int_{0}^{\infty} ist}\left(\dfrac{
 even if spawn_link fails, and loGs it in our pHoeniX loGs, iT wOuld Do)

A:

STarting a procesS UsinG spawn_link/1 will cause a biDirecTiONal lINk, So whiChever oF ThE SPawNiNg ProCeSS aNd the NewLy spawnEd process tHat HaPpens to die fiRSt Will kill thE otHer one (unless It's TrappiNg ExiTS, whicH it ProbaBly shoULdn't be). that's greaT iN Some caSEs, and noT SO gReat In others; if it takes A LoNG time to send thaT e-mail, FoR ExAMPle, The phoenix reqUeSt migHT finish FIrST, ANd rISk killing off tHe spawned prOCesS.
Due to ThE liNKing, hoWever, ThERe sHouldn't be anY risK of the proCesses GEtting oRPhaned.
A Better AppRoaCh is DEfInIteLy TO crEAtE a SUPerVisor (or uSiNg task.SUperVISOR), and You CoulD roll Your own backgrOunD job SEtuP rathEr easIly.
HOwEver, iT might Be worTh Looking at somethIng lIke exq thaT yoU mEntIoNed, or tOniq foR exAmpLe, that cOuld posSIblY hAVE EvErything you need alrEaDY; EsPecially Things LIkE rETries in cAsE of FailURE, and pResiSTeNce. There Are alsO SoMe Other inTeRestinG oPtiOns In the aWesoMe ElixIr list if You waNT to try out a few dIFferent alternATiVES.

 Q:

hOw to CalCulate FouriEr trANsfoRm of THiS fuNCtion?

The fuNcTIoN Is given by $$f(t)=\dfrac{1}{e^{at}-1}$$
noW, i know From tHe definition i'Ve to evaluaTE THis integRal $$\bEGiN{Align}\mathcal{F}[f(T)]&=\int_{0}^{\iNfty}e^{-j \omegA T}\left(\dfrAc{1}{e^{at}-1}\Right)\,dt \\&=\sUm_{n=1}^{\infty}\iNT_{0}^{\Infty}e^{-t(j\OmeGa+aN)}\,dt \\&=\Sum_{N=1}^{\INfTy}\dfrac{1}{j\omega+AN}\End{aLiGn}$$
Is it tHe rIght way To aPprOacH? 

A:

AS fAr as I can tEll, the inTeGrAl DiVerGes, buT Here's how OnE caN aTtaCk the PRoblem Using KnowN FOuRIer transfoRM pAIRs anD FOuRier traNsForm tHeorEMs.
I Assume $a > 0$, $h(t)$ is the HeAvySIde uNiT sTep funcTion, and I'll use ThE substitutIoN $\omEga = 2\pi s$ TO Use the FoUrier Transform form with wHIch I'm moSt cOmforTablE.
$$I = \int_{0}^{\inftY} e^{-2\pI ist}\leFt(\dFRac{
 even if spawn_link fails,  and logsit in  ou r p ho enix  log s, it would do ) 

A: 

Starting a process u singsp a wn_l i nk /1 wi ll caus e  a b idi re ct ion al li nk, s o w hicheve r of the s paw ni ng process a n dthe newlyspa wned process  th at hap pe nst o die  fi rst w ill ki l l theother one  ( u nlessi t's tra p p in g ex its, which it pro b ab l y shouldn't be ). Tha t' s  g r e atinsome cases ,and n o t so gr e at i n  ot h ers; if it ta kes a longt ime  to se nd  th a t e-ma il, f or exa mple, the P hoen ix reques t migh t  finish first,and ri skkil ling of fthe  s p awn e dpro c ess .
Due to  t he  link ing, h o w ever , t here  shou ldn't be anyris k of the  proc esses  get ti ng or phaned .
A b et ter approach is  def initely t o c re ate  a  Supe r visor(or  us ing Tas k.Super v iso r) , a nd  you could roll yo ur o wn  backgro und jo b  s et u p rather  e asi ly.H o wever , it mi ght be w orth l o ok in g at so me thingli keexq  that youmentio ned, orToniq for example, t h at could poss i bl y ha v e ev ery thing you n eeda lrea dy;e sp eci a lly t hings  l i ke retries in case offa ilure,  andpresistence.There area l s o some o ther in t eresting optio ns in  the Aweso m e Elixir  list  if youwant to t r y  out a f ewdif fer ent a lt ernatives.

Q : 

Ho wto calc ula te Four ier  tr ans for mof this f unction? 
th efu nct ion i s  given b y$$f (t )=\ dfrac { 1}{e^{ at}-1 }$$No w, i k now fro m  t h e  def in it ioni'v eto ev alua t e t his int egral $$\ beg i n{al ig n} \mathca l{F}[f(t)]&=\ in t_{0}^{\in ft y}e ^{-j \ o m ega t}\l eft(\dfrac{1}{e^{at}-1} \ right)\ ,dt  \\&= \sum _{n=1}^{\ inf ty}\in t_{ 0 }^{\in fty}e^ {-t(j \o meg a + an)}\ , d t\\& =\ sum_{n=1}^ { \ inf ty}\d fr ac{1 }{j\ome ga+an}\end{align}$ $ 
Is  it the right  wa y to a pp roa c h? 

A :Asf a r as I can tell , the inte gr a ldiverges,b uthe re's ho w one c an at t ack the  problemusing kno wn  Fou r i erTransformpairs an d Fourier Trans f or m the ore ms.
Ias sum e $a> 0$,$ H(t )$ is  the H ea vyside  unit  s tep func tion, and I'll use thesubsti tutio n $ \omega =2\p i  s$  to use t he F ourier Tra nsf orm  form  wi t h whi ch I ' mmos t  comf orta b le.
$$I = \i nt_ { 0 }^ {\infty} e^ { - 2 \pi  ist} \le f t(\dfr ac{
 even_if spawn_link_fails, and logs it_in our_phoenix_logs, it_would_do)

A:

Starting a process_using spawn_link/1 will_cause a bidirectional link,_so whichever of_the_spawning process and the newly spawned process that happens to die first will kill_the_other one_(unless_it's_trapping exits, which it probably_shouldn't be). That's great in_some cases,_and not so great in others; if it_takes_a long time_to send that e-mail, for example, the Phoenix request_might finish first, and risk killing_off the spawned_process.
Due_to_the linking, however, there_shouldn't be any risk of the_processes getting orphaned.
A better approach is_definitely to create a Supervisor (or using_Task.Supervisor), and you could roll your_own background job setup rather_easily.
However, it_might be worth looking at_something like exq_that you_mentioned, or Toniq_for example, that could possibly have_everything you need_already; especially things like retries in_case_of failure, and_presistence._There_are also_some other interesting_options_in the_Awesome_Elixir list if you want to_try_out a few different alternatives.

 Q:

How to_calculate Fourier transform of_this_function?

the function is given_by $$f(t)=\dfrac{1}{e^{at}-1}$$
Now, i know from_the definition i've to evaluate this_integral $$\begin{align}\mathcal{F}[f(t)]&=\int_{0}^{\infty}e^{-j_\omega t}\left(\dfrac{1}{e^{at}-1}\right)\,dt_\\&=\sum_{n=1}^{\infty}\int_{0}^{\infty}e^{-t(j\omega+an)}\,dt \\&=\sum_{n=1}^{\infty}\dfrac{1}{j\omega+an}\end{align}$$
Is it the right way to approach? 

A:

As far as_I can tell, the integral diverges,_but here's how one_can attack_the_problem using known_Fourier_Transform pairs_and Fourier Transform theorems.
I assume $a >_0$, $H(t)$_is the Heavyside unit step function,_and I'll use the_substitution_$\omega = 2\pi s$ to use_the Fourier Transform form with which_I'm most comfortable.
$$I = \int_{0}^{\infty}_e^{-2\pi_ist}\left(\dfrac{