Elementary Functions - 4.12 Generalized Logarithms and Exponentials

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.12.E1	${\displaystyle{\displaystyle\phi(x+1)=e^{\phi(x)}}}$ \phi(x+1) = e^{\phi(x)}	${\displaystyle{\displaystyle-1<x,x<\infty}}$	phi(x + 1) = exp(phi(x))	\[Phi][x + 1] == Exp[\[Phi][x]]	Skipped - no semantic math	Skipped - no semantic math	-	-
4.12.E2	${\displaystyle{\displaystyle\phi(0)=0}}$ \phi(0) = 0		phi(0) = 0	\[Phi][0] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
4.12.E3	${\displaystyle{\displaystyle\psi(e^{x})=1+\psi(x)}}$ \psi(e^{x}) = 1+\psi(x)	${\displaystyle{\displaystyle-\infty<x,x<\infty}}$	psi(exp(x)) = 1 + psi(x)	\[Psi][Exp[x]] == 1 + \[Psi][x]	Skipped - no semantic math	Skipped - no semantic math	-	-
4.12.E4	${\displaystyle{\displaystyle\psi(0)=0}}$ \psi(0) = 0		psi(0) = 0	\[Psi][0] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
4.12.E5	${\displaystyle{\displaystyle\phi(x)=\psi(x)}}$ \phi(x) = \psi(x)	${\displaystyle{\displaystyle 0\leq x,x\leq 1}}$	phi(x) = psi(x)	\[Phi][x] == \[Psi][x]	Skipped - no semantic math	Skipped - no semantic math	-	-
4.12.E6	${\displaystyle{\displaystyle\phi(x)=\ln\left(x+1\right)}}$ \phi(x) = \ln@{x+1}	${\displaystyle{\displaystyle-1<x,x<0}}$	phi(x) = ln(x + 1)	\[Phi][x] == Log[x + 1]	Failure	Failure	Error	Skip - No test values generated
4.12.E8	${\displaystyle{\displaystyle\psi(x)=e^{x}-1}}$ \psi(x) = e^{x}-1	${\displaystyle{\displaystyle-\infty<x,x<0}}$	psi(x) = exp(x)- 1	\[Psi][x] == Exp[x]- 1	Skipped - no semantic math	Skipped - no semantic math	-	-