XΒ²+XY=ln(Y)
Domain coloring of the principal branch of the Lambert W function
Hello everyone. A couple of you may recall that my earlier Lambert W function uploads were missing the negative real axis. That was because the formula I had adapted diverged at the negative real values, and I couldn't find a way to patch for that yet. However, by adapting Dr. IstvΓ‘n MezΕ's formula I came across in Wikipedia (this would be the link of the actual paper: https://www.researchgate.net/publication/346668850_An_integral_representation_for_the_Lambert_W_function) with some complex parameterization technique, I was able to gain full access to the principal branch of the function: https://www.desmos.com/calculator/9gj8swotjh?lang=en (2D on real axis), https://www.desmos.com/calculator/nx9run7gnf?lang=en (Domain coloring on the complex plane). I'm still working on finding and adapting the full generalized Lambert W that I could use to plot all branches, but it felt so great to finally achieve the negative real axis of the principal branch, so I wanted to share it with you. I hope you enjoy.
Hello everyone. 5 days ago, I had posted the completed principal branch of the Lambert W function. Now, I present you with the model that works for all branches of the Lambert W function, with the slider k for finding the different branches. The red part are the real values, and the blue the imaginary. I based this on this formula in the Wolfram Alpha website: wolframalpha.com/input/?i=W%280%2C-1%29; however, one thing to note is that the formula in Wolfram has an error because it lacks a negative sign in front of the i/2pi, which should have been there (I checked several times to make sure), and I corrected for that. In case some user here is affiliated with Wolfram Alpha by chance, perhaps you can send them a message to tell them about it. Meanwhile, the caveat of this formula is that it can't be trusted on the interval [-1/e, 0] because it follows different rules, as you may be able to notice from my graph of the principal branch here that displays the values that should be happening for W(-1,x). I'm starting to develop a hypothesis on why this may be the case, which may allow me to design a piecewise function for this region that works with the rest of the graph if it is valid, because from my observations I'm guessing it may just be that the formula is simply giving me values of different branches for that zone instead of just random or completely wrong values. Anyway, here is the functional model without further ado: https://www.desmos.com/calculator/tepnenoovs?lang=en. Feel free to compare it with my earlier Lambert W principal branch model, or simply x = ye^y. I hope you enjoy.
Hello everyone. Just as an open question, does there happen to be someone who happen to know some explicit formulation for W(-1,z)? The formula I have for W(0,z) has served me quite well in my recent experiments, including this one (https://www.desmos.com/calculator/x9fcckoh4i?lang=en), but I could never find an expression for the other branches like W(-1,z), which I feel may help me unlock some missing pieces of the puzzle. Do you think you could offer me some advice, at least on where I could try to look?
I'm having some trouble with a differentiation.
I know that if one has W(x), where W is the Lambert W function,
W'(x) = W(x) / (x (1+W(x))
My question is, what if we must find the derivative of W(f(x))?
Does this become:
W(f(x)) / [f(x) (1 + W(x))] * f'(x)
This would be my intuition but I can't seem to find this case after some searching around. I suppose I am most unsure as to whether x is replaced by f(x) in the denominator.
Domain coloring of W(-1,z) (The \"white snowdots\" are not part of the actual)
Hello everyone. A couple days ago, I had posted a formula that could be used for all branches of the Lambert W function except at the interval [-1/e,0]. Now, I have double-checked and patched for that interval with a piecewise function so that we could have the full, uninhibited Lambert W. From graphical analysis via my domain coloring model, cross-checks with the Wolfram Alpha calculator, and mathematical analysis, I realized that the only thing I needed to patch for was that strip of real value inputs between [-1/e,0] for k = 0 and -1 (switching what should have happened for k = 0 to k = -1 and vice versa), so I did by writing specific conditionals for those two situations only. Now we have W(k,x) (https://www.desmos.com/calculator/dzn2y7o6oi?lang=en), domain coloring of W(k,z) (https://www.desmos.com/calculator/h5cz1ztcww?lang=en), and of course, the full Lambert W calculator (https://www.desmos.com/calculator/cpro1gwimb?lang=en). The W(k,x) and the Lambert W calculator work relatively quickly, especially the Lambert W calculator, but for the domain coloring model, adding additional conditionals appears to also compromise speed; however, it still only takes like 1~2 minutes to appear and a little less to change with differing values of k on my computer. The thing that puzzles me though is that small undefined dots can emerge on the domain coloring model, but from what I know the Lambert W calculator itself works fine even at those values, and the dots appear and disappear at different "zoom ins" I implement, so I assume they are just artefacts. As for the Lambert W calculator itself, I may have to look for a way to define the value of W(0,0) and find out why the imaginary numbers, though very tiny enough to be ignored, appear for the interval [-1/e,0] when they should be just 0, even though the real part works just fine (or I might not because I already have a very effective function for the principal branch of the Lambert W, a
... keep reading on reddit β‘Iβve found some online that involve Stirlingβs approximation, but they all have Lambertβs W function, and I would like to know if thereβs an approximation to Lambertβs W function.
Regarding locating roots of an equation, how would one use the Lambert W Function to locate these roots. I have tried for resources and read online about explanations but the methods taken rather confuse me.
e.g. Solve 2^x = x + 4
I have put the equation into a functions, where f(x) = 2^x - x - 4, and set f(x) =0.
I found the roots basically by trial and error since using logs didn't work and ended up with x values:
One root of f(x) in the interval 2 < x < 3
Another root of f(x) in the interval -4 < x < -3
I then improved the root:
x = 2.5 --> x < 0
x = 2.75 --> x < 0
x = 2.8 --> x > 0
x = 2.775 --> x > 0
x = 2.7625 --> x > 0
x = 2.75625 --> x > 0
and so on but I concluded that the root of the first equation was in the interval 2.75 < x < 2.75625.
and similarly for the other root which I located in the interval -3.9375 < x < -3.935
I wanted a method that was a less "try your luck" kind of method that gave a more exact value, whereby I found the Lambert W Function; however, I have no clue how it works apart from the concept that it uses complex numbers to find real roots (unless I understood the concept wrong). I used symbolab to give a representation of the method but it did not help much. How would one use the Lambert W Function in this instance to work out the root.
This is from Paul Hsieh's website:
Lambert's W function is defined as follows: W(x)e^(W(x)) = x. Prove that lim_(x->inf) W(x)/(ln(x)-ln(ln(x)) = 1.
edits: formatting
And why doesn't it have those?
I think it might be showing up in my research and I'd like to learn more about it beyond the minimal wikipedia article. Does anybody have any resources aimed at beginning grads/late undergrads with a basic complex analysis background?
I'm going to be honest and say I don't know THAT much about math (I've taken up to Calculus 3 in college). I am trying to make a spreadsheet using Google that calculates what level you are, from what experience you have in a video game called RuneScape. The top image is the function to calculate how much experience you have, given what level you are, x. I thought it would be relatively simple to just solve for x however when I tried to do that in WolframAlpha, it gave me the function in the bottom image where x is the level you are and y is the amount of experience you have.
The problem comes in when Wolfram spits out this equation with a W sub n in it. I have no idea what that means but Wolfram told me that it is the Lambert W-Function. I was wondering if any of you know a way that I can either input the Lambert W-Function into Google Sheet or find a way to solve the top equation for x without using the Lambert W-Function. And you'd get bonus points for ELI5 what the Lambert W-Function is.
I know that it's used to solve functions of the form ex^x but I still have no idea what it represents, nor how to actually calculate it. Also I don't understand what the "branches" of the W function mean or represent. Thanks in advance.
Okay, so I recently tried to solve a problem that involves finding the inverse of f(x)=x+ce^x where c is some constant, and I was told about the Lambert W function (W(x)), which is the inverse of the function f(x)=xe^x. I was able to find that the answer I was looking for was y=ln(W(ce^x)/c).
This got me thinking, though. A couple of times in the past, Iβve run into problems where Iβve had to find the inverse of x-csin(x) (like with Kepler orbits) or x-csinh(x) (like with Catenary arcs). Since both of these functions can be written using exponents, I was wondering if there was some way to rearrange the Lambert W function so it can be used as a solution to x-csin(x), or x-csinh(x), or x-ccos(x), etc..
If anyone might have advice for how to approach this, or if any of you may have by chance already come up with a solution yourselves, thatβd be great. Just to let you know, this isnβt a homework problem or anything, so there might not be a guaranteed solution, I was just hoping someone could help me look into this.
Thanks guys!
So, you are given the simple equation to solve: 2^x-2=x. The obvious first answer to this is 2^2-2=2, ie 4-2=2.
But what about the negative solution? x~=-1.69009. Functions of this form (and many others) require the use of the function 'W': https://en.wikipedia.org/wiki/Lambert_W_function Can someone please ELI5 this?
EDIT: Another use of this function is solving: a^b=b^a Obviously a=2, b=4 is one solution, but what about any further solutions?
Thanks!
I am very very new to any coding at all and was trying to solve this non-continuous compound interest equation for all variables and I figured out all but n. N is the compounding rate/year. y=P(1+r/n)t*n I put in in wolfram alpha (solving for n) and it gave me this: http://imgur.com/9Wr95fZ How do I use the W function in python?
Oh, and c is any arbitrary constant.
http://en.wikipedia.org/wiki/Lambert_w_function
I have been reading some papers with the hopes of conducting research in the near future. The topic I want to research uses the Lambert function. I was hoping that someone could help me understand important aspects of the Lambert function.
EDIT: My question is with regards to projectile motion in resisting medium. The papers I have read use it in their mathematical analysis.
A worksheet my math teach handed out included the problem 7^(x-2)=5x. Although it was a typo (it should have been 7^(x-2)=5^x), I looked into solving the original. It appears to solve 7^(x-2)=5x you need use of Lambert W functions. Can anyone explain them to me (or other ways to solve the problem)?
Team Taz (outside of Hook) has been taking major Lβs since the Darby feud. Even giving Lβs amongst each other when Cage and Starks were beefing.
Lambertβs guys and MotY have not exactly picked up a major win either.
I think Lambert and Taz are brilliant on the mic. But they each need a big win to brag about and rub in. Maybe Hook will break this, and the two stables can form an alliance.
Note: This is about symbolic variables and functions (syms).
I'm attempting to solve an equation that should return a more complex version of the Lambert W function, if it is indeed solvable. It seems to me that I may be able to find a solution, but MatLab is not returning one. However, a scaled down version also returns nothing, but it returns the basic Lambert W function in Wolfram Alpha. Of course, the latter isn't powerful enough to compute my complex one, so it doesn't help me there. I spent some time reading about the Lambert W function, and MatLab does have a command that outputs values of the function for any input, but it doesn't seem to be able to spit it out as a result from the "solve" command. If anyone has any experience here, I'd appreciate some help!
Disclaimer: I'm an economist, but I have a BS in Math.
Hello fountain pen flex writers, another great quality flex pen here. The Aikin (unknown why there's the mis spelling of Aiken, as Waterman was in control of company during this time? If any experts would like to chime in that would be awesome) 14k wasn't pure enough to be considered gold in Euro market, required minimum of 18K, hence the reason for the 18K nib. Original cap clip is missing, but there is a Mabie Todd & Co Ltd "Clipper" Accomodation clip on it in place of it
All purchases must be made through PayPal Goods and Services, per r/penswap rules. Price includes priority shipping through USPS, with insurance at value of pen and tracking. Shipping included only applies to buyers in CONUS. I am willing to ship Internationally at buyers risk and expense. Please reply in post prior to sending direct message. Thanks for your time, in checking out this post.
Verification, Album and Writing Sample: https://imgur.com/a/Jc3339Y
Mid 1920s- Early 1930's Aikin Lambert & Co Capitols Fountain Pen in Black/Gray Marbled Celluloid, LF, w/ 18K Capitols Fine Full Flex nib (Rated D, due to age, wear and non original parts. Ink sac is in great shape. Nib writes a fine line without pressure and up to a BB with medium pressure. Fantastic pen. Has MT&CLtd Accomodation clip. Asking $95.00 Shipped CONUS ONLY OBO. Reduced to $85.00 Shipped CONUS ONLY, REDUCED AGAIN TO $75.00 w/ Shipping CONUS ONLY
Feel free to ask any questions you may have Thanks for checking out this post! Stay Safe and Happy Writing
Hi guys, I plan on signing up for some Spanish courses this year but am not sure which of the two organisations to go for:
I'm leaning towards CVO semper as it seems to only have very good reviews and seems to really cater for students, the downside being that it's twice as expensive as the alternative offered by CCLM which seems to have generally good reviews, but not as ideal as CVO semper.
Can anyone help a brother out with some advice/past experiences if you followed courses in either institution please?
Thanks for taking the time to read this!
This is the first post I've seen of this watch on the sub, so feel free to look it over if you're interested in this rep!
Update: it's been GL'd! Thanks for all the input.
Dealer name: Jtime
Factory name: APSF
Model name (& version number): Black Ceramic Audemars Piguet Royal Oak Perpetual Calendar (v2 w/ GMT Function)
Album Links: https://imgur.com/a/NjE1w96
Index alignment: Visually looks good though technically the 3 o'clock marker is a bit low. No issues for me here.
Dial Printing: Looks noice; on par with example pics from Jtime's website
Date Wheel alignment/printing: N/A
Hand Alignment: On fleek, I believe
Bezel: Looks good, screws look aligned properly as well
Solid End Links (SELs): Screws look a bit too inset on the 6 o'clock side, but that's inconsequential
Timegrapher numbers: -5 s/d; Amplitude: 302 ; Beat Error: 0.1 ms
Price Paid: $758 + $45 shipping (then 5% off with Wise payment)
u/WatchYoda your gracious input would be greatly appreciated
Seems odd that when they complain the alcohol runs out, my Alcoholic Geralt doesn't bother mentioning that he's carrying a whole inn's worth of drink
https://preview.redd.it/vutbtxu6h7e81.png?width=388&format=png&auto=webp&s=6049a95a79daeb38756f5b07724391055bee7d67
Yes, Iβm fully on board with the criticisms of him being the mouthpiece for Men of the Year, but last night Dan was fucking fire on the mic. An economy of words, eloquent, succinct and sharp. Just a masterclass that Heenan would prob even be proud of.
Edit: His hoodie last night also looked cozy as hell.
I have been reading some papers with the hopes of conducting research in the near future. The topic I want to research uses the Lambert function. I was hoping that someone could help me understand important aspects of the Lambert function. My question is with regards to projectile motion in resisting medium. The papers I have read use it in their mathematical analysis.
