Difference between revisions of "Manuals/calci/PENTATE"

Revision as of 12:43, 29 August 2017

PENTATE (a,n)

This function shows the value of Pentation of given numbers.
In $PENTATE(a,n)$ , $a$ and $n$ are any real numbers.
Pentation is indicating the fifth hyper operator.
The most common notation for pentate is used by Knuth's up-arrow notation as $a\uparrow \uparrow \uparrow b$ or $a\uparrow ^{3}b$ or a^^^b .
It can also be notated a{3}b in Bowers operator notation.
Normally notation can be continued for $a^{b}$ for exponents and $^{b}a$ for teteration and a(*)b for pentation.
Pentation has the following properties:a^^(a^^^b) = a^^^(b+1), and (a^^^b)^^^c ~< a^^^(b+c).
But other than that, it has even fewer nice properties than tetration has.
Some examples of Pentation are given below:

@@ Line 7: / Line 7: @@
 *Pentation is indicating the fifth hyper operator.
 *The most common notation for  pentate is used by Knuth's up-arrow notation as <math>a \uarr \uarr \uarr b </math> or <math>a\uarr^3 b</math> or a^^^b .
-*It can also be notated <math>a{{3}}b</math> in Bowers operator notation.
+*It can also be notated '''a{3}b''' in Bowers operator notation.
 *Normally notation can be continued for <math>a^b</math> for exponents and <math>^b a</math> for teteration and a(*)b for pentation.
 *Pentation has the following properties:a^^(a^^^b) = a^^^(b+1), and (a^^^b)^^^c ~< a^^^(b+c).