how-to-get-exert-value-of-a-lambert-w-function-question-without-wolfram-alpha-

Question Number 142679 by Gbenga last updated on 03/Jun/21

h o w t o g e t e x e r t v a l u e o f a l a m b e r t w f u n c t i o n q u e s t i o n w i t h o u t w o l f r a m a l p h a

Commented by Dwaipayan Shikari last updated on 03/Jun/21

W (x) = \underset{n = 1}{\sum^{\infty}} \frac{{(- n)}^{n - 1}}{n!} x^{n}

Commented by Gbenga last updated on 03/Jun/21

e x a m p l e p l e a s e

Commented by Dwaipayan Shikari last updated on 03/Jun/21

x^{x} = 2

x l o g (x) = l o g (2)

e^{l o g (x)} l o g (x) = l o g (2)

l o g (x) = W_{0} (l o g (2))

x = e x p (W_{0} (l o g (2)))

x = e x p (l o g (2) - {l o g}^{2} (2) + \frac{3}{2} {l o g}^{3} (2) - \dots)

Commented by Gbenga last updated on 03/Jun/21

- w h a t i s n o w t h e v a l u e o f x

Commented by Gbenga last updated on 03/Jun/21

4^{x = 4 x}

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