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+--- Thread: product tetration (/showthread.php?tid=1808)
product tetration - Alex Zuma 2025 - 09/24/2025
product tetration is the superfunction of \(f(x)=xa^{x}\).
it uses the lambert w function (also known as the product logarithm) to go in the negative direction.
product tetration requires three variables and is denoted as: \(\text{prodtet}(a,b,c)\)
product tetration can be interpolated through lagrange polynomials for extension to real numbers.
and it has this recursive property:
\(\text{prodtet}(a,b,c)= f(\text{prodtet}(a,b,c-1))\)
and this base case:
\(\text{prodtet}(a,b,0)= b\)
more details are given on this desmos graph: https://www.desmos.com/calculator/cnvdx5ce1r