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

Related Videos

Exponents

See Also


References