View source for fu'a'ai

==== valsi ====
fu'a'ai
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Sun Feb 23 18:49:16 2014
 
== English ==
=== Definition #53091 - Preferred ===
 
==== selma'o ====
PA5
==== definition ====

digit/number: first Foias' constant; the unique value of <span class="MATH"><i>x</i><sub>1</sub></span> such that  MATH
 $x_n\to\infty$
 
<span class="MATH"><i>x</i><sub>n</sub>→∞</span> as  MATH
 $n\to\infty$
 
<span class="MATH"><i>n</i>→∞</span> for  MATH
 $x_{n+1}  = \left(1 + \frac1{x_n}\right)^n$
 
<span class="MATH"><i>x</i><sub>n+1</sub> = <img alt="$\left(\vphantom{1 + \frac1{x_n}}\right.$" src="/jbovlaste_export/GP6K3XmjKz/img1.png" style="height: 4.27ex; vertical-align: -1.63ex; "/>1 + <img alt="${\frac{1}{{x_n}}}$" src="/jbovlaste_export/GP6K3XmjKz/img2.png" style="height: 3.15ex; vertical-align: -1.15ex; "/><img alt="$\left.\vphantom{1 + \frac1{x_n}}\right)^{n}_{}$" src="/jbovlaste_export/GP6K3XmjKz/img3.png" style="height: 4.41ex; vertical-align: -1.74ex; "/></span>; such <span class="MATH"><i>x</i><sub>1</sub></span> = 1.187…

==== notes ====
See also: [[fu'a'au|fu'a'au]]
==== gloss words ====

<ul><li>[[natlang/en/first Foias' constant|first Foias' constant ; ≈ 1.187...]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
3
     
==== time ====
Mon Aug 11 21:57:55 2025



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=== Etymology ===