-Trigonometric and -Hyperbolic Functions in Complex Domain

Pseudocode 3

Mathematica v. 9.0 code. Function sh3inv returns values of for using inversion of the formula (36) for . This approach provides more precision than solving differential equation.

In2  :=  auxAgSh3s_?NumberQ  :=

   s Hypergeometric2F11/3,  1/3, 1 + 1/3,  -s3

(* assigns definition to auxiliar function auxAgSh3 *)

In3  :=  sh3invx_?NumericQ  :=

   (s/. FindRootauxAgSh3s  -  x, s, 0, -1, 20)

(* assigns definition to function sh3inv *)

In4  :=  Plot

   sh3invx,  x, -pip3, 2,

   PlotStyle -> Thick,  PlotRange  -> -2, 7

(* plots the graph *)