How do you use Lambert W?
How do you use Lambert W?
Lambert W function
- The Lambert W function is used in mathematics to solve equations in which the unknown appears both outside and inside an exponential function or a logarithm, such as 3x + 2 = ex or x = ln(4x).
- The Lambert W function is defined as the multivalued function W that satisfies.
- for any complex number .
What is AW function in math?
The Lambert W function (red curves) is defined by the equation WeW = x. The direct function (left) maps values of W to values of x, whereas the inverse function (right), which is of greater mathematical interest, takes x as the input and computes the corresponding value of W.
What is W in complex numbers?
The number a is called the real part of a + bi, and b is called its imaginary part. Traditionally the letters z and w are used to stand for complex numbers. The plane in which one plot these complex numbers is called the Complex plane, or Argand plane.
How much is the number Omega?
Ω = 0.567143290409783872999968662210… (sequence A030178 in the OEIS). 1/Ω = 1.763222834351896710225201776951…
What log10 means?
n. (Mathematics) a logarithm to the base ten. Usually written log or log10. Compare natural logarithm.
What is 4i in math?
So, the square root of -16 is 4i. All negative square roots are called “imaginary numbers” (now you know where that letter ‘i’ comes from). Complex Numbers. When a number has the form a + bi (a real number plus an imaginary number) it is called a “complex number”.
What is the Lambert W-function?
Lambert W-Function. The Lambert -function, also called the omega function, is the inverse function of. The plot above shows the function along the real axis. The principal value of the Lambert -function is implemented in the Wolfram Language as ProductLog [ z ].
How is the Lambert -function implemented in the Wolfram Language?
The plot above shows the function along the real axis. The principal value of the Lambert -function is implemented in the Wolfram Language as ProductLog [ z ]. Different branches of the function are available in the Wolfram Language as ProductLog [ k, z ], where is any integer and corresponds to the principal value.
Is the Lambert function over the complex plane?
The Lambert -function is illustrated above in the complex plane. The real (left) and imaginary (right) parts of the analytic continuation of over the complex plane are illustrated above (M. Trott, pers. comm.). is real for . It has the special values
Where can I find the formula for calculating W(A)$?
I strongly suggest you have a look at http://en.wikipedia.org/wiki/Lambert_W_function. In the paragraph entitled “Numerical evaluation”, they give Newton and Halley formulae (the latest one has been massively used by Corless et al. to compute $W(a)$.
