How-Can-derive-LambertW-z-in-the-Form-of-integral-W-z-1-pi-0-pi-ln-1-z-sin-t-t-e-t-cot-t-dt-z-1-e-Or-Similar-to-the-example-LambertW-z-How-other-Functions-can-be-Derived-

Question Number 204573 by MathedUp last updated on 22/Feb/24

How Can derive LambertW (z) in the

Form of integral ? ? ?

W (z) = \frac{1}{π} \int_{0}^{π} \ln (1 + \frac{z \cdot \sin (t)}{t} e^{t \cdot \cot (t)}) d t, z \in [- \frac{1}{e}, \infty)

Or Similar to the example . LambertW (z)

How other Functions can be Derived in Integral Form

Commented by TonyCWX08 last updated on 22/Feb/24

T h a n k y o u f o r t h i s

Commented by mr W last updated on 22/Feb/24

i s R a m b e r t t h e s a m e p e r s o n a s

L a m b e r t ?

Commented by MathedUp last updated on 22/Feb/24

Oops \dots Rambert \to Lambert