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Created page with "<div style="font-size:30px">'''PENTATE (a,n)'''</div><br/> *<math>a</math> and <math>n</math> are any real numbers. ==Description== *This function shows the value of Pentati..."
<div style="font-size:30px">'''PENTATE (a,n)'''</div><br/>
*<math>a</math> and <math>n</math> are any real numbers.
==Description==
*This function shows the value of Pentation of given numbers.
*In <math>PENTATE(a,n)</math>,<math>a</math> and <math>n</math> 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 <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.
*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).
*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
==See Also==
*[[Manuals/calci/TETRATE| TETRATE]]
*[[Manuals/calci/SLOG| SLOG]]
*[[Manuals/calci/SUPERLOGARITHM| SUPERLOGARITHM]]
==References==
*[https://sites.google.com/site/pointlesslargenumberstuff/home/2/uparrows Pentate]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]
*<math>a</math> and <math>n</math> are any real numbers.
==Description==
*This function shows the value of Pentation of given numbers.
*In <math>PENTATE(a,n)</math>,<math>a</math> and <math>n</math> 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 <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.
*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).
*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
==See Also==
*[[Manuals/calci/TETRATE| TETRATE]]
*[[Manuals/calci/SLOG| SLOG]]
*[[Manuals/calci/SUPERLOGARITHM| SUPERLOGARITHM]]
==References==
*[https://sites.google.com/site/pointlesslargenumberstuff/home/2/uparrows Pentate]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]