Lambert W Function - Special Values

Special Values

For any non-zero algebraic number x, W(x) is a transcendental number. We can show this by contradiction: If W(x) were non-zero and algebraic (note that if x is non-zero then W(x) must be non-zero as well), then by the Lindemann–Weierstrass theorem, eW(x) must be transcendental, implying that x=W(x)eW(x) must also be transcendental, contradicting the condition that x is algebraic.

(the Omega constant)

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