These are the commands used to define transcendental functions.
func(x) :: func(x)'/x' = expression
Where expression is a function of func(x) and/or x, defines the differential equation for func.
inv ::~ func; inv(x) ::~ expression;
Defines inv as the inverse of func or expression.
func(const1) ::= const2
Where const1 and const2 evaluate to constants, sets an initial condition for the differential equation defining func.
The order in which initial conditions are defined matters; the first initial condition defined is used to vet potential solutions for differential equations.
init.math also defines expression-valued integer recurrences which generate the reduction of a transcendental function composed with an integer multiple of its inverse function. It should be possible to generate these recurrences from the differential equations, but this is yet to be done.