Calculate an Exponential Tower

Calculator for exponential towers. An exponential tower is a sequence of exponentiations, like a₁ to the power of (a₂ to the power of (a₃ to the (...))). The single steps are determined by a sequence, this can also simply be a number. As running variable, which is increased by 1 in each step, i is used. Only this variable may occur in the formation sequence. The basic arithmetic operations + - * / are allowed, as well as the power function, like pow(2#i) for 2ⁱ. Further allowed functions are sin(), cos(), tan(), asin(), acos(), atan(), log() for the natural logarithm and abs() for the absolute value. Also, the constants e and pi can be used. If every step is a number larger than 1, the result will get very big very quickly. If one step is negative and its exponential is an even root, the value and its following values can't be calculated.

The exponentiation is calculated from top to bottom, so a_n-1 to the power of a_n, then a_n-2 to the power of the previous result, and so on, until a₁ to the power of ...

If the formation sequence is a number a and m=1, the exponential tower can be written in Knuth's up-arrow notation as a ↑↑ n.

Examples:

• a_i = 2: 2 ↑↑ 2 = 4; 2 ↑↑ 3 = 16 and 2 ↑↑ 4 = 65536. For the next value, the result will be so big that Infinity is shown. 2 ↑↑ 5 would have 19728 places.
• a_i = 1.715*abs(sin(x)): This exponential tower slowly converges to the value 2.5233822195973...

The arrow notation was developed in 1976 by computer scientist Donald E. Knuth and is a method for representing very large numbers. Here, ↑ stands for the power, so a↑b = a^b. ↑↑ is the exponential tower, so a↑↑b = (a↑a↑a↑...)[b times a]. More than two arrows in a row are also possible in this notation, but they cannot be calculated with this calculator. The problem with very large numbers is anyway that, although they can be represented, they cannot be calculated exactly, even with the best computers.