Hyper-L Notation

Hyper-Log notation or Hyper-L notation is an extension of the Log function that itself is a fast growing function, but not fast enough.Hyper-L Notation - Jonathan's Googology Hyper-L notation is as follows. The standard notation is L(n) to indicate it is a hyper-L function.
== First Order ==
Representation: L(n)
Rule: \(L(n)\) = \(Antilog(n)\), also known as \(10^n\)
Examples:
*\(L(5)\) = 100,000
*\(L(33)\) = decillion
*\(L(100)\) = googol
*\(L(googol)\) = googolplex
== Second Order ==
Representation: \(L((n))\)
Rule: \(L((n))\) = \(10^{Antilog(n)^{Antilog(n)^{...^{Antilog(n)}}}}; where ...=Antilog(n)\)
Examples:
*L((3)) = \(10^{1000^{1000^{...^{1000}}}} (... = 1{,}000)\)
*L((5)) = \(10^{100,000^{100,000^{...^{100,000}}}} (... = 100{,}000)\)
*L((33)) = \(10^{\text{decillion}^{\text{decillion}^{...^{\text{decillion}}}}} (... = \text{decillion})\)
*L((100)) = \(10^{\text{googol}^{\text{googol}^{\text{googol}^{...^{\text{googol}}}}}} (... = \text{googol})\)
*L((googol)) = \(10^{\text{googolplex}^{\text{googolplex}^{...^{\text{googolplex}}}}} (... = \text{googolplex})\)
== Third Order ==
Representation: L(((n)))
Rule: \(L(((n))) = 10\uparrow^{Antilog(n)}Antilog(n)\)
Examples:
*L(((5))) = \(10\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{100{,}000}100{,}000\)
*L(((33))) = \(10\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\text{decillion}}\text{decillion}\)
*L(((100))) = \(10\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\text{googol}}\text{googol}\)
*L(((googol))) = \(10\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{\text{googolplex}}\text{googolplex}\)
== Approximations ==
For first order (\(L(n)\)):
Notation 	Lower bound 	Upper bound
Hyper-E notation	E(n) 	E(n)
Arrow notation 	\(10\uparrow n\)	\(10\uparrow n\)
== Sources ==
Category:Notations
Category:Notations by JTOnstead20
Category:Functions