AGM_FUNCTION _ _ _ _ _ _ _ _ _ _ _ _ operator

The AGM_function operator returns a list of (N, AGM, list of aNtoa0, list of bNtob0, list of cNtoc0) where a0, b0 and c0 are the initial values; N is the index number of the last term used to generate the AGM. AGM is the Arithmetic Geometric Mean.

syntax:

examples:

AGM_function(1,1,1) 

  1,1,1,1,1,1,0,1  


AGM_function(1, 0.1, 1.3) 

  {6,
   2.27985615996629, 
   {2.27985615996629, 2.27985615996629,
    2.2798561599706, 2.2798624278857, 
    2.28742283656583, 2.55, 1},
   {2.27985615996629, 2.27985615996629,
    2.27985615996198, 2.2798498920555, 
    2.27230201920557, 2.02484567313166, 4.1},
   {0, 4.30803136219904e-12, 0.0000062679151007581,
    0.00756040868012758, 0.262577163434171, - 1.55, 5.9}}

The other Jacobi functions use this function with initial values a0=1, b0=sqrt(1-m), c0=sqrt(m).