1. Online calculator for fast-growing hierarchy with Extended Buchholz Function

For calculation of expressions of fast-growing hierarchy write below a natural number n>0 and a countable ordinal α written in the normal form for Extended Buchholz Function, i.e. α=0 or α=ψ₀(β₁)+...+ψ₀(β_k), where k≥1 and ψ₀(β₁)≥...≥ψ₀(β_k) and β_i∈C₀(β_i) for 1≤i≤k. Each β_i also should be written in the normal form, i.e. β_i=0 or β_i=ψ_ν1(γ₁)+...+ψ_νm(γ_m). Write "_{" before each subscript and "}" after it, even if this subscript is just 0. Don't use spaces. Write "p" instead of "ψ". A non-zero finite ordinal μ in the line for α should be written as p_{0}(0)+...+p_{0}(0) where p_{0}(0) repeats μ times. For example, instead of ψ₀(ψ₁(0)+ψ₁(0)) write p_{0}(p_{p_{0}(0)}(0)+p_{p_{0}(0)}(0)). Some other examples of α you can find here. See also video with examples of work

n =

α =

2. Online calculator for Extended Arrows with Extended Buchholz Function

For calculation of expressions of Extended Arrows write below positive integers b, c and a countable ordinal α written in the normal form for Extended Buchholz Function. The requirements for filling in the line for α are the same as in case of the previous calculator.

b = ; c =

α =