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Super-exponentiation

Super-exponentiation (a@b) can be defined inductively as a@(b-1) raised to the power a, where a@1 is a.

Then the operation @ follows exponentiation in the sequence

addition a+b,

multiplication a*b,

exponentiation ''ab,

each one inductively defined from the binary operation before.

Source

The source of this notation is http://mathforum.org/library/drmath/view/54586.html.

Some values

1@2 = 1

2@2 = 4

3@2 = 27

4@2 = 256

5@2 = 3125

6@2 = 46,656

7@2 = 823,543

8@2 = 16,777,216

9@2 = 387,420,489

10@2 = 10,000,000,000

11@2 = 285,311,670,611

12@2 = 8,916,100,448,256

13@2 = 302,875,106,592,253

1@3 = 1

2@3 = 16

3@3 = 7,625,597,484,987

1@4 = 1

2@4 = 65,536

2@5 = A number with nearly 20,000 digits

1@n = 1 for all non-negative integers

n@1 = n for all real numbers

n@0 = 1 for all real numbers

n@(-1) = 0 for all real numbers not equal to 1

n@(-2) = negative infinity for all real numbers greater than 1

n@(-2) = infinity for all real numbers between 0 and 1





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