# Manuals/calci/PENTATE

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**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:

- 2^^^1 = 2^^(2^^0) = 2^^1 = 2.
- 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536

## Examples

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

## Related Videos

## See Also

## References