# Manuals/calci/PENTATE

PENTATE (a,n)

• and are any real numbers.

## Description

• This function shows the value of Pentation of given numbers.
• In , and 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 or or a^^^b .
• It can also be notated a{3}b in Bowers operator notation.
• Normally notation can be continued for for exponents and 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:
1. 2^^^1 = 2^^(2^^0) = 2^^1 = 2.
2. 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536

## Examples

1. PENTATE(3,2) = 7625597484987
2. PENTATE(4,1) = 4
3. PENTATE(1,3) = 1
4. PENTATE(5,2) = Infinity

Exponents