| Omega Constant |
Article Index for Omega |
Website Links For Omega |
Information AboutOmega Constant |
| CATEGORIES ABOUT OMEGA CONSTANT | |
| irrational numbers | |
| mathematical constants | |
| omega | |
|
:. It is the value of ''W''(1) where ''W'' is Lambert's W Function . The name is derived from the alternate name for Lambert's ''W'' function, the ''Omega function''. The value of Ω is approximately 0.5671432904097838729999686622. It has properties that are akin to those of the Golden Ratio , in that : or equivalently, : One can calculate Ω Iteratively , by starting with an initial guess Ω0, and considering the Sequence : This sequence will Converge towards Ω as ''n''→∞. IRRATIONALITY Ω can be proven Irrational from the fact that E is Transcendental ; if Ω were rational, then there would exist integers ''p'' and ''q'' such that : so that : : and e would therefore be algebraic of degree ''p''. However e is transcendental, so Ω must be irrational. Ω is in fact Transcendental as the direct consequence of Lindemann–Weierstrass Theorem . SEE ALSO EXTERNAL LINKS |
|
|