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)
Read more about this topic: Lambert W Function
Famous quotes containing the words special and/or values:
“We cannot set aside an hour for discussion with our children and hope that it will be a time of deep encounter. The special moments of intimacy are more likely to happen while baking a cake together, or playing hide and seek, or just sitting in the waiting room of the orthodontist.”
—Neil Kurshan (20th century)
“We cannot spare our children the influence of harmful values by turning off the television any more than we can keep them home forever or revamp the world before they get there. Merely keeping them in the dark is no protection and, in fact, can make them vulnerable and immature.”
—Polly Berrien Berends (20th century)