Tetration/Related Articles

See also changes related to Tetration, or pages that link to Tetration or to this page or whose text contains "Tetration".

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Parent topics

• Mathematical function [r]: Dependence between two quantities, one of which is given. ^[e]
• Superfunction [r]: For given function $f$, solution $F$ of equation $F(z\!+\!1)=f(F(z))$ ^[e]

Other related topics

• Exp [r]: $f=\exp$ is the only solution of equations $~f^{\prime }(z)\!=\!f(z)~\forall z\in \mathbb {C} ~$ and $~f(0)\!=\!1$. ^[e]
• Holomorphic function [r]: Function $f$ from $A\subseteq \mathbb {C}$ to $B\subseteq \mathbb {C}$ is called holomorphic in domain $A$ if for every open domain $E\subseteq A$ there exist derivative $f'(z)~\forall ~z\in E$. ^[e]
• Biholomorphism [r]: Property of a holomorphic function $f$ from $A\subseteq \mathbb {C}$ to $B\subseteq \mathbb {C}$

characterized in that there exist holomorphic function $g=f^{-1}$ : $f{\big (}g(z){\big )}\!=\!z~\forall z\in B~$ and $g{\big (}f(z){\big )}\!=\!z~\forall z\in A~$. ^[e]

• Ackermann functions [r]: Mathematical function $A$ of two variables, such that for integer arguments $n,n$ it can be expressed as follows:

$A(m,n)={\begin{cases}n+1&{\mbox{if }}m=0\\A(m-1,1)&{\mbox{if }}m>0{\mbox{ and }}n=0\\A(m-1,A(m,n-1))&{\mbox{if }}m>0{\mbox{ and }}n>0.\end{cases}}$. ^[e]

• Fixed point [r]: A point in the domain of a function that is mapped to itself by the function, i.e., a point x such that f(x) = x. ^[e]
• Mathematical notations [r]: Professional slang used by researchers, especially in mathematical publications and presentations. ^[e]
• Superfunction [r]: For given function $f$, solution $F$ of equation $F(z\!+\!1)=f(F(z))$ ^[e]
• Transfercunction [r]: Function that expresses the output of some physical or mathematical object for the given input. ^[e]