-Trigonometric and -Hyperbolic Functions in Complex Domain

Pseudocode 2

Mathematica, v. 9.0 code. Code for pipp_ computes for given argument . Code for s3x_ computes for , code for sh3x_ computes for , and code for sin3x_ computes real-valued function for .

In1  :=  pipp_  =

   Integrate1/(1 - sp)(1/p), s, 0, 1,

     Assumptions -> p > 1

(* assigns definition to function pip which returns pi_p/2 *)

Out1  =  

In2  :=  s3x_  =  (ux/.

     NDSolve

     ux  ==  (vx)(1/2), vx  ==  - 2 ux2,

      u0  ==  0, v0  ==  1,

     u, v, x, -5, pip31)

(* assigns definition to auxiliar function s3 *)

In3  :=  sh3x_  = (ux/.

     NDSolve

     ux  ==  (vx)(1/2), vx ==  2 ux2,

      u0 ==  0, v0  ==  1,

     u, v, x, -pip3, 5 1)

(* assigns definition to auxiliar function sh3 *)

In4  :=  sin3x_  =  (ux/.

     NDSolveux  ==  (Absvx)(1/2) Signvx,

          vx  ==  -2 Absux*ux,

          u0  ==  0, v0  ==  1,

          u,v, x, -4 pip3, 4 pip31)

(* assigns definition to auxiliar function sin3 *)