Modified exponential summation
Sum of the series $\sum _{ r=1 }^{ \infty }{ \frac { { r }^{ 3 } }{ r! } } $
How does background blur (bokeh) relate to sensor size? This is a somewhat theoretical question.  Suppose I first take a photo of a subject using a full frame sensor DSLR, with a given lens (say 50mm prime lens at f/3.5).  Now suppose I exchange the camera for an APS-C sensor DSLR (with a 1.6× crop factor). I keep the same lens (same focal length, same aperture) and I step back a few meters in order to maintain the field of view (at least keep the same magnification of the subject). I now take a second photo.  Clearly depth of field will have increased between the two photos. But what about background blur (for example, trees at infinity)? Will I have the same amount of background blur, or will that have changed?  I have read somewhere that background blur depends on the physical aperture size. In this case the physical aperture (physical focal length divided by f/stop) stays the same. But should this number be taken in relation to the sensor size? In which case with the smaller APS-C sensor, the physical aperture will be relatively bigger, which would mean more background blur. This would be rather counter-intuitive as we usually consider it to be more difficult to get background blur on an APS-C camera.  Please give the reasoning behind the answer. I would answer the question myself using this  but I can't manage to get it to run on my computer. Period detection of a generic time series I have a polygon shapefile of many lakes, I also have a point shapefile of locations on those lakes where fish were caught.  The point shapefile contains the attributes: Fisherman_iD, Fish_Caught, Lat, Long.  The polygon shapefile contains the attributes Lake_name, Points_per_polygon(PNTCNT)  Each point obviously has differing entries under the fish_caught field.   What I want to get is the average fish caught per lake (polygon).  So I need to have a total number of fish caught, per individual polygon, and then I can divide that by the PNTCNT file I create using the Points in a Polygon tool.  Ideas? I am relatively new to QGIS. I'm a begginer in blender, so please forgive me if the question looks silly to you!  Almost all the objects in my scene disappeared (except 2) as if I deleted them by mistake. The thing is all the objects are still listed in the right side graph. The all have the eye button activated, but yet nothing is visible anymore! As I don't have a backup file, I simply can't find any tricks to fix this...  Thank you for you help! Let $X_1$ and $X_2$ be independent and identically distributed exponential random variables with rate $\lambda$. Let $S_2 = X_1 + X_2$.  Q: Show that $S_2$ has PDF $f_{S_2}(x) = \lambda^2 x \text{e}^{-\lambda x},\, x\ge 0$.  Note that if events occurred according to a Poisson Process (PP) with rate $\lambda$, $S_2$ would represent the time of the 2nd event.   Alternate approaches are appreciated. The approaches provided are commonly used when learning queueing theory &amp; stochastic processes.     Recall the Exponential distribution is a special case of the Gamma distribution (with shape parameter $1$). I've learned there is a more general version of this  that can be applied. Is Borden's true identity real, or another ruse? Towards the end of , it's revealed that Borden accomplishes his Transported Man trick by using his twin brother, Fallon, as a double. It then becomes clear that he has been doing this in his personal life as well as on stage - each brother leads 'half a life', sometimes appearing as Borden and sometimes as Fallon. This is how he completes the illusion: one Borden goes into the first door, the other Borden emerges from the second door a moment later. Angier doesn't know how Borden does the trick, and doesn't believe Borden uses a double despite being told as much by Cutter. He follows what he believes to be a clue in Borden's notebook and travels to Colorado to meet Nikola Tesla, who Angier believes can build a machine that can help him perform the trick. Angier believes that Tesla built a similar machine for Borden. However, the final pages of the notebook reveal that Tesla was merely a red herring, designed to get Angier out of Borden's way for a long time. Tesla, it turns out, had never built such a machine before. At this point, Tesla agrees to build Angier's machine anyway. Instead of building a machine that transports matter, he builds one that duplicates it. Angier uses this machine in his act, but in order to avoid having to deal with multiple clones (the &quot;prestige materials&quot;), one of them must die as part of the act. This all makes sense, so far, but I find it hard to believe that Borden's use of the word 'Tesla' as the key to his cipher is random. It's too coincidental that he sends Angier on a wild goose chase, but Angier returns with a working machine. A film that is otherwise so tightly plotted shouldn't rely on coincidence to move the narrative forward, so there must be something else going on. Is it possible that Borden cloned himself using Tesla's machine? After upgrade of any app - apps move back from SD Card to phone memory.  After that, to save phone memory, I have to move upgraded app back to SD card.   Is any possibility to avoid this because it is very annoying?  I have Android 5.0.2 on Motorola E second gen phone. Estimate on the derivative at fixed point Let $D$ be a bounded domain and let $f$ be analytic function from $D$ into $D$. Show that if $z_{0}$ $\in D$ is a fixed point for $f$ , then $|f' (z_{0} )| \leq 1$.  WHAT I WAS THINKING:   To have a conformal mapping from $D$ to the unit disc &amp; after composing it with $f$ ; I was thinking to use Pick's Lemma. So, can anyone tell me any conformal map from any bounded domain to the unit disc?? OR Is there any other way out to solve this problem?? Ok. I was playing mcpe and I noticed that mossy cobblestone isn't in the crafting table. And I wanted to make a house that looks old. So if its possible to get mossy cobblestone without mods, how can I get it on survival? If it is possible can somebody please leave a step by step guide. Thank you. Refreshing a question doesn't update the answer count properly In the Stack Exchange Android App v1.0.7 1.0.33 (with a HTC One running Android 4.4.2), the answer count for a question you're viewing is displayed in two places:   In the label of the answer tab:   At the bottom of the question tab:    I've noticed that these counts don't reliably update when new answers arrive.   If you refresh the question tab, neither count updates. If you refresh the answer tab, the second count will be updated, but the answer tab's count will not, leaving the two out of sync.   Refreshing either tab should probably update both counts!    Screenshots of the bug in action:    I waited for it to be answered. A while later, the question now has an answer.    The tab still says 0 answers though. Switching back to the question tab, , but the tab count still doesn't. Solve for $x$ in the $80^\circ$-$80^\circ$-$20^\circ$ triangle I've been solving this for days but I still I couldn't solve this. Can I know how to solve $x$ ? $(document) vs. $("document") When I run this command :  apt install libkf5*   I get the following error :  Unable to locate package libkf5*    I'm sure that the packages whose names start with libkf5 exist (tab-completion says so) . So the problem is not about the absence of those packages.(Note the asterisk at the end of that error message , the wildcard's not working at all) I use apt v.1.9. Thanks in advance. Is it possible to produce a context free grammar for Tikz path? node? Even further, I would be happy to see a definition of the tikz language in the usual manner programming languages such as Java and Pascal are defined.   The reason I ask is that I keep getting mysterious error messages for the tiniest typos. Essentially, incorrect use of the underlying languages leads to a "crash" of the compiler. This crash sometimes gives useful error messages, but sometimes they are hard to decipher. Detecting the system DPI/PPI from JS/CSS? I'm working on a kind of unique app which needs to generate images at specific resolutions according to the device they are displayed on. So the output is different on a regular Windows browser (96ppi), iPhone (163ppi), Android G1 (180ppi), and other devices. I'm wondering if there's a way to detect this automatically.  My initial research seems to say no. The only suggestion I've seen is to make an element whose width is specified as "1in" in CSS, then check its offsetWidth (see also ). Makes sense, but iPhone is lying to me with that technique, saying it's 96ppi.  Another approach might be to get the dimensions of the display in inches and then divide by the width in pixels, but I'm not sure how to do that either. How to create a table with long text and which packages use How do I move Ubuntu dock to bottom on Ubuntu 17.10 and later? I stupidly ran sudo chown -R carlos:carlos / and carlos is my user. This changed all files to be Carlos and I could not boot up again (because the root files were now owned by #1000) and I cant get sudo acess in live cd (because the owner of /usr was changed to my user). Can anyone help me? FYI I have mounted my hard drive. "Much more easy" versus "much easier" Where does Google Chrome automatically save pages? I opened the following page:   When disconnecting WiFi and even after rebooting the mobile phone, the page can still be read due to being saved automatically.  Left to the URL bar, an indicator looks like this:  This also shows up when opening manually saved pages, which are saved as MHTML files in the default download folder.  However, an automatically saved page can not be re-downloaded manually to get to the download folder, because the arrow is greyed out.I wish to copy some automatically saved pages into the download folder.  Where are the files of automatically saved pages stored?