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The gaitrol is equal to $$\{10,100,7 (1) 3\}$$ in BEAF.[1] The term was coined by Jonathan Bowers.

### Approximations and exact values in other notations

Notation Approximation
Bird's array notation $$\{10,100,7 [2] 3\}$$ (exact)
Cascading-E notation $$\textrm E100\#\text{^}\#100\#\text{^}\#100\#\#7$$
Hyperfactorial array notation $$100![7,2,1,2]$$
Fast-growing hierarchy $$f_{(\omega^{\omega}) 2+6}(100)$$
Hardy hierarchy $$H_{\omega^{(\omega^{\omega}) 2+6}}(100)$$
Slow-growing hierarchy $$g_{\vartheta((\Omega^\Omega) 2+5)}(100)$$

### Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2014.

Jonathan Bowers' googol series

Googol series: googol(plex/duplex/triplex/quadraplex/quinplex) · giggol(plex/duplex) · gaggol(plex/duplex) · geegol(plex) · gigol(plex) · goggol(plex) · gagol(plex)
Boogol series: boogol(plex/duplex/triplex) · biggol(plex/duplex) · baggol(plex) · beegol(plex) · bigol · boggol · bagol
Troogol series: troogol(plex/duplex) · triggol(plex/duplex) · traggol(plex/duplex) · treegol · trigol · troggol · tragol
Quintoogol series: quintoogol(plex) · quintiggol · quintaggol · quinteegol · quintigol · quintoggol · quintagol · (sextoogol · septoogol · octoogol)
Goobol series: goobol(plex) · gibbol · gabbol · geebol · gibol · gobbol · gabol
Boobol series: boobol · bibbol · babbol · beebol · bibol · bobbol · babol
Troobol series: troobol · tribbol · trabbol