In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function f(w) = wew, where w is any complex number and ew is the exponential function. For each integer k there is one branch, denoted by Wk(z), which is a complex-valued function of one complex argument. W0 is known as the principal branch. These functions have the following property: if z and w are any complex numbers, then holds if and only if When dealing with real numbers only, the two branches W0 and W−1 suffice: for real numbers x and y the equation can be solved for y only if x ≥ −1/e; we get y = W0(x) if x ≥ 0 and the two values y = W0(x) and y = W−1(x) if −1/e ≤ x < 0. The Lambert W relation cannot be expressed in terms of elementary functions. It is useful in combinatorics, for instance, in the enumeration of trees. It can be used to solve various equations involving exponentials (e.g. the maxima of the Planck, Bose–Einstein, and Fermi–Dirac distributions) and also occurs in the solution of delay differential equations, such as y′(t) = a y(t − 1). In biochemistry, and in particular enzyme kinetics, an opened-form solution for the time-course kinetics analysis of Michaelis–Menten kinetics is described in terms of the Lambert W function. (Wikipedia).
The Lambert W Function Introduction
This function comes up as a solution to equations ranging from pure math to quantum physics to biology. In this video, I introduce the concepts behind the function and give some sample calculations. There's lots more to this function, so explore it on your own if you're interested.
From playlist Math
Lambert W Function Intro & x^x=2
Lecture on Lambert W, 1/5/2021 https://youtu.be/Qb7JITsbyKs ☀️ Patreon: https://www.patreon.com/blackpenredpen 😃 https://blackpenredpen.com 😃 https://twitter.com/blackpenredpen 😃 https://www.instagram.com/blackpenredpen/ #LambertWfunction #tetration
From playlist Lambert W Function
2 different exponential equations
We will solve 2 different exponential equations: x^2*e^x=2 and x+e^x=2 by using the Lambert W function. Solving equations with Lambert W functions, Lambert W function Intro: https://youtu.be/sWgNCra93D8 Derivative of Lambert W function, https://youtu.be/LyEPB6Wxc_U Solve x*e^x=1 by using
From playlist Lambert W Function
Derivative of Lambertghini W function, FAST
Derivatives for you T shirt, https://teespring.com/derivatives-for-you Intro to Lambert W function, https://youtu.be/sWgNCra93D8 Please subscribe for more math content! ☀️support bprp on Patreon: https://www.patreon.com/blackpenredpen Guess what my first job was! https://youtu.be/RSCzX
From playlist Lambert W Function
how to find a complex solution for e^x=ln(x)
We will solve an interesting algebraic equation involving both exponential and logarithm, namely e^x=ln(x). Although the graphs of y=e^x and y=ln(x) do not intercept, we can actually find some complex solutions to this equation. We do need to use the Lambert W function tho. So see here for
From playlist Lambert W Function
Integrating the Lambert W-Function
Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Integrate Inverse: https://www.youtube.com/watch?v=sejU9qnRcRE This is like ,,Part 2" of my series where we are going to be discussing some things revolving around
From playlist Integrals
Cool Math: The Lambert W Function and Infinite Tetration
Here is one of many applications of the Lambert W function in calculating the value of converging tetrations (hyper-4 operator), or "power towers". Tetration is also explained here, so don't worry if you have never heard of them! Watch the Lambert W function appear before your very eyes!
From playlist Math
Solve x^x^x=2 | Newton's Method
Can we use the Lambert W function to solve this? I do not know the answer but I used the Newton's Method. : ) Lambert W function intro: https://youtu.be/sWgNCra93D8 Newton's Method: https://youtu.be/EjUp_5X6io4 Derivative of x^x^x https://youtu.be/UJ3Ahpcvmf8 Tetration equation, newton's
From playlist Lambert W Function
Super Exponential Cubic Equations!
We will solve two "super" exponential cubic equations x^x^3=2 and x^x^3=3. We will need to use the Lambert W function for one of them! Hello~ 0:00 solving x^x^3=2 0:33 solving x^x^3=3 3:52 Lambert W function (aka productlog) intro: https://youtu.be/sWgNCra93D8 **The Satisfyingly St
From playlist Lambert W Function
x^y=y^x and its Amazing Solutions.
Support the channel by signing up on Brilliant for FREE using the link https://brilliant.org/FlammableMaths ! =D @FlammableMathsTwo69 Gone Wrong Done Right Playlist: https://www.youtube.com/playlist?list=PLN2B6ZNu6xmekOYxY25OQcaG_nkmw1hKv Lambert W: https://youtu.be/CX-5orQxNAg Today we
From playlist Mathematics Gone Wrong Done Right
Press F to pay respects to Papa Lambert [ integral W(1/x^2) from 0 to infinity ]
Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Gaussian integral: https://www.youtube.com/watch?v=g-Et3vIbJdE Hypervolume integral: https://www.youtube.com/watch?v=b-u-ML8PQeo Welcome back dudes and dudettes :v
From playlist Integrals
The Lambert W Function's Derivative
Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Let us calculate this bad boi's derivative using implicit differentiation. Also providing you with a graphical representation to show you, in which situation said d
From playlist Random problems
Come be bored with me...and math! (The Dream Stream)
Fielding questions from my subscribers! Can you figure out any patterns in the coefficients from the end of the stream? Stay tuned for more videos soon!
From playlist Quarantstreams
Ome-god! A stunning integral - Wacky Calc Wednesday
I love you, please subscribe: https://www.youtube.com/channel/UClMCwEEK5Xfm7OMGjW0FYzQ?view_as=subscriber Instagram: https://www.instagram.com/whatthehectogon/ Email: whatthehectagon@gmail.com I've been waiting to do this integral for so long! It's a truly magnificent result, and a gre
From playlist Wacky Calc Wednesdays
Wacky Calc [Friday]: The Lambert W Function
Like, comment, subscribe! Instagram: https://www.instagram.com/whatthehectogon/ Email (yes, it is misspelled): whatthehectagon@gmail.com Hellooooo! Finally, the prodigal son returns with a great lil wacky calc video not at all on it's intended day of release. This is quite an old
From playlist Wacky Calc Wednesdays
From playlist Quarantstreams
infinite power tower of i, namely i^i^i^... We will need the lambert W function If you enjoy my videos, then you can click here to subscribe https://www.youtube.com/blackpenredpen?sub_confirmation=1 T-shirts: https://teespring.com/stores/blackpenredpen Patreon: https://www.patreon.com/bl
From playlist Lambert W Function
The Wltimate Integral Part 1: The Setup - Wacky Calc Wednesdays
Blessed are those who like and subscribe: https://www.youtube.com/channel/UClMCwEEK5Xfm7OMGjW0FYzQ?view_as=subscriber Instagram: https://www.instagram.com/whatthehectogon/ Email: whatthehectagon@gmail.com Finally, we are addressing this big fat elephant in the room, THE integral of integ
From playlist Wacky Calc Wednesdays