How do I get from $ \int_{0}^{1}{t^{x-1} (1-t)^{y-1}\,\mathrm dt} $  to $ \displaystyle\int_{0}^{\infty}{ \frac{t^{x-1} + t^{y-1}}{(1+t)^{x+y}} \,\mathrm dt} $ ? I have tried different change of variables but without success.
How do I get from   $$B(\alpha,\beta)=\int_{0}^{1}{ t^{ \alpha -1}  (1-t)^{ \beta -1} \,dt}$$ to:   $$2^{2- \alpha - \beta } \int_{0}^{ \infty}{ \frac{ \cosh (( \alpha - \beta )x)}{( \cosh(x))^{ \alpha + \beta }} \,dx}$$  ? I have tried different change of variables such as $t=1- \frac{1}{ \cosh (x)}$ and got $\int_{0}^{ \infty}{ \frac{ \sinh (x)  ( \cosh (x)-1)^{ \alpha -1} }{( \cosh(x))^{ \alpha + \beta }} \,dx}$ but without success.
Cancellation of addition on convex sets I  found a question about a property of the . However the question was not properly answered (it used a projection argument which might not be true in a general Banach space).  I was wondering whether the following (weaker) statement holds:  Let $X$ be a Banach space and suppose $A,B,C_0\subset X$ are bounded, closed, convex and non-empty subset. Do we then have $$A+C_0=B+C_0\implies A=B?$$ How do I enable the "multiverse" repository? I keep seeing places refer to the "multiverse" repository as a place I can get software, how can I enable this repository? Please specify how to do this graphically and via command line. How strong of magnetic field would noticibly attract a person? There is iron in our blood, which is magnetic. Roughly how strong would a magnet have to be to induce a noticeable attraction? It would be nice to know this for several distances. Also, do electromagnets that strong exist? I bought two pieces of land. One from Morthal, and one from Falkreath. Morthal was the first plot of land I purchased. I only finished half of it. I bought the plot of land in falkreath because I liked the nature better. I finished the house completely in Falkreath. Every time I try to adopt a child off the streets it keeps saying "I have a place but no room for you" Even though I have the bedrooms in my Falkreath house. Why can I not adopt a child and have him/her live at my house in Falkreath? What does a leading zero do for a php int? Why do most C programmers name variables like this:  int *myVariable;   rather than like this:  int* myVariable;   Both are valid. It seems to me that the asterisk is a part of the type, not a part of the variable name. Can anyone explain this logic? how to copy or backup files ignoring dot files Intel Corporation Device [8086:0d4f] is not supported on Ubuntu 18.04.3 I am currently unable to install ubuntu server 18.04.03 LTS on the latest intel NUC10i7FNH.  Ubuntu always states both network adapters as unclaimed. The previous version (NUC8i7BEH) has the same network controller I219-V and worked like a charm.  *-network:0 UNCLAIMED      description:  Network controller      product: Intel Corporation      vendor: Intel Corporation      physical id: 14.3      ...   Without network it is not even possible to follow most suggestions how to get it enabled, because it is impossible to fetch new packages from internet.  Here are some more information as requested:  The output from: modprobe -v e1000e &amp;&amp; dmesg | grep e10   [ 3447.889394] e1000e: Intel(R) PRO/1000 Network Driver - 3.2.6-k [ 3447.889395] e1000e: Copyright(c) 1999 - 2015 Intel Corporation.   The output from: sudo lspci -knn  00:1f.6 Ethernet controller [0200]: Intel Corporation Device [8086:0d4f]     Subsystem: Intel Corporation Device [8086:2081] 01:00.0 PCI bridge [0604]: Intel Corporation JHL7540 Thunderbolt 3 Bridge [Titan Ridge 2C 2018] [8086:15e7] (rev 06)    For me this looks somehow, as the kernal driver would not be in use :-/  Here are a few more information i got from playiung around with 19.10 desktop version.  [    0.000000] Linux version 5.3.0-29-generic (buildd@lcy01-amd64-024) (gcc version 9.2.1 20191008 (Ubuntu 9.2.1-9ubuntu2)) #31-Ubuntu SMP Fri Jan 17 17:27:26 UTC 2020 (Ubuntu 5.3.0-29.31-generic 5.3.13)   output from lshw:    *-network:0        Beschreibung: Kabellose Verbindung        Produkt: Intel Corporation        Hersteller: Intel Corporation        Physische ID: 14.3        Bus-Informationen: pci@0000:00:14.3        Logischer Name: wlp0s20f3        Version: 00        Seriennummer: c8:09:a8:9c:cd:e0        Breite: 64 bits        Takt: 33MHz        Fähigkeiten: pm msi pciexpress msix bus_master cap_list ethernet physical wireless        Konfiguration: broadcast=yes driver=iwlwifi driverversion=5.3.0-29-generic firmware=48.4fa0041f.0 ip=192.168.178.109 latency=0 link=yes multicast=yes wireless=IEEE 802.11        Ressourcen: iomemory:600-5ff irq:16 memory:6023114000-6023117fff   The output from: modprobe -v e1000e &amp;&amp; dmesg | grep e10  [    2.357430] e1000e: Intel(R) PRO/1000 Network Driver - 3.2.6-k [    2.357430] e1000e: Copyright(c) 1999 - 2015 Intel Corporation. [    2.357616] e1000e 0000:00:1f.6: Interrupt Throttling Rate (ints/sec) set to dynamic conservative mode [    2.562796] e1000e 0000:00:1f.6 0000:00:1f.6 (uninitialized): registered PHC clock [    2.634139] e1000e 0000:00:1f.6 eth0: (PCI Express:2.5GT/s:Width x1) 1c:69:7a:60:44:f0 [    2.634140] e1000e 0000:00:1f.6 eth0: Intel(R) PRO/1000 Network Connection [    2.634258] e1000e 0000:00:1f.6 eth0: MAC: 13, PHY: 12, PBA No: FFFFFF-0FF [    2.634991] e1000e 0000:00:1f.6 eno1: renamed from eth0 [    5.103285] checking generic (4000000000 e10000) vs hw (4000000000 10000000) [   15.806697] e1000e: eno1 NIC Link is Up 1000 Mbps Full Duplex, Flow Control: None    output from lspci:  00:1f.6 Ethernet controller [0200]: Intel Corporation Ethernet Connection (10) I219-V [8086:0d4f]     DeviceName:  LAN     Subsystem: Intel Corporation Ethernet Connection (10) I219-V [8086:2081]     Kernel driver in use: e1000e     Kernel modules: e1000e Classify all groups with order $pq$, $p$ is not equal to $q$ I am reading the following material:  . At page 5, there is a proof classifying all groups with order $pq$(they are all primes and $p$ is not equal to $q$). I am lost in the last two sentence, which claims the semidirect product are all isomorphic. Could someone help me to understand it? Thanks! \documentclass{minimal} \usepackage{tikz} \begin{document} \pgfmathparse{random(-5,5)} \pgfmathresult \end{document}   Works, but I have a .0.0 that not supposed to be here. Why is defragmentation unnecessary? Why is defragmenting unnecessary in Ubuntu? Foo* set = new Foo[100]; // ... delete [] set;   You don't pass the array's boundaries to delete[]. But where is that information stored? Is it standardised? What exactly can a financial advisor do for me, and is it worth the money? I've been managing my own expenses pretty meticulously for the past 4-5 years since being out of college and on my own. Because of this, I feel I have more of a clue about finances than the average 28-year-old.  I use  to manage pretty much all of my accounts, though I realize this is just a quick and easy personal finance solution. Plus, there's no personally customized advice on how I invest or set up my monthly budget.  These are the reasons I think I may want to find a good financial advisor. However, I don't know what I don't know. That is, there could be a long list of things I should be doing with my money to plan for retirement or just for general financial wellbeing.  Are these the functions of a financial advisor? What can I expect if I sit down to meet with one? Most importantly, how much would I be paying for this advice and is it worth it? Historical flight data outside of the USA? The question  only deals with flights in the US sourced from the  . Is there some similar source for EU, Asia etc? In JavaScript:  encodeURIComponent("©√") == "%C2%A9%E2%88%9A"   Is there an equivalent for C# applications? For escaping HTML characters I used:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"&amp;#" + ((int)m.Value[0]).ToString() + ";");   But I'm not sure how to convert the match to the correct hexadecimal format that JS uses. For example this code:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"%" + String.Format("{0:x}", ((int)m.Value[0])));   Returns "%a9%221a" for "©√" instead of "%C2%A9%E2%88%9A". It looks like I need to split the string up into bytes or something.  Edit: This is for a windows app, the only items available in System.Web are: AspNetHostingPermission, AspNetHostingPermissionAttribute, and AspNetHostingPermissionLevel. android expandablelistview how to set space between groups items The generating function for the Fibonacci numbers I am not able to find an answer to the following question:     For which positive even integers $k$ is the integer   $$p^2+k$$ prime, where $p$ is a prime number $\gt5$? How to remove conference information from the ACM 2017 SIGCONF template? Who made the decision for Gandalf's promotion from 'grey' to 'white'? In the first book of the LoTR, after his fight with the Balrog of Moria, Gandalf the Grey changed to .   My question is, who made the decision to 'promote' him from grey to white? Was it ? Or was it the ? Or was it the ?