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:
“He’s leaving Germany by special request of the Nazi government. First he sends a dispatch about Danzig and how 10,000 German tourists are pouring into the city every day with butterfly nets in their hands and submachine guns in their knapsacks. They warn him right then. What does he do next? Goes to a reception at von Ribbentropf’s and keeps yelling for gefilte fish!”
—Billy Wilder (b. 1906)
“What we often take to be family values—the work ethic, honesty, clean living, marital fidelity, and individual responsibility—are in fact social, religious, or cultural values. To be sure, these values are transmitted by parents to their children and are familial in that sense. They do not, however, originate within the family. It is the value of close relationships with other family members, and the importance of these bonds relative to other needs.”
—David Elkind (20th century)