Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Taylor series of i[x]
#8
Big Grin 
Okey, here is a website: http://jwbales.us/ where you can calculate the sign by a programme. I checked the source of it, and I take the important part of it out. You can read it at the bottom.
I have made an own java html code, and it works. So we have a recursive formula for the signs. The next question is how to make just one formula and how to interpolate (to reals) and extrapolate (to complexes).
We are really close to have its Taylor series!

Code:
function bitValue(number,bit){

var result = (number & (1<<bit)) >>> bit;
return result;
}

function twist(p,q){
var state="A0";
var pbit=0;
var qbit=0;
var result=1;
var p0=p;
var q0=q;
var pplus=1+p0;
var qplus=1+q0;
var stateA0 = [];
var stateA  = [];
var stateB  = [];
var stateNB = [];
var stateC  = [];
var stateNC = [];
var loopIndex=Math.ceil(Math.LOG2E*Math.log((Math.max(pplus,qplus))));
var pXORq =eval(p0) ^ eval(q0);
stateA0[0] = "A0"
stateA0[1] = "A"
stateA0[2] = "B"
stateA0[3] = "NB"

stateA[0]  = "A";
stateA[1]  = "A";
stateA[2]  = "C";
stateA[3]  = "NC";

stateB[0]  = "B";
stateB[1]  = "NC";
stateB[2]  = "B";
stateB[3]  = "C";

stateNB[0] = "NB";
stateNB[1] = "C";
stateNB[2] = "NC";
stateNB[3] = "NB";

stateC[0]  = "C";
stateC[1]  = "NC";
stateC[2]  = "NC";
stateC[3]  = "NC";

stateNC[0] = "NC";
stateNC[1] = "C";
stateNC[2] = "C";
stateNC[3] = "C";

if (p < 0 || q < 0){
p=p0;
  q=q0;
  str = "Values of p and q cannot be negative!";
  alert(str);
}

for (var i = 0; i < loopIndex; i++){
   var j = loopIndex - i - 1;
   var k = 2*bitValue(p,j)+bitValue(q,j);
   if (state == 'C'){
       state = stateC[k];
       continue;
   }
   if (state == 'NC'){
       state = stateNC[k];
       continue;
   }
   if (state == 'B'){
       state = stateB[k];
       continue;
   }
   if (state == 'NB'){
       state = stateNB[k];
       continue;
   }
   if (state == 'A'){
       state = stateA[k];
       continue;
   }
   if (state == 'A0'){
       state = stateA0[k];
       continue;
   }
}
   if (state=="NB" || state=="NC") {
       result="-1";
   }
   return result;    
}
Xorter Unizo
Reply


Messages In This Thread
Taylor series of i[x] - by Xorter - 01/12/2017, 04:50 PM
RE: Taylor series of i[x] - by sheldonison - 01/12/2017, 08:50 PM
RE: Taylor series of i[x] - by Xorter - 01/13/2017, 05:26 PM
RE: Taylor series of i[x] - by Xorter - 01/13/2017, 07:13 PM
RE: Taylor series of i[x] - by Xorter - 01/14/2017, 10:14 AM
RE: Taylor series of i[x] - by mike3 - 01/23/2017, 07:38 AM
RE: Taylor series of i[x] - by Xorter - 02/26/2017, 11:10 AM
RE: Taylor series of i[x] - by Xorter - 03/01/2017, 03:06 PM
RE: Taylor series of i[x] - by Xorter - 03/04/2017, 09:40 AM
RE: Taylor series of i[x] - by Xorter - 04/06/2017, 03:42 PM
RE: Taylor series of i[x] - by Xorter - 04/11/2017, 12:18 PM
RE: Taylor series of i[x] - by Xorter - 07/10/2017, 04:07 PM
RE: Taylor series of i[x] - by Xorter - 02/20/2018, 09:55 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 4,158 03/21/2020, 08:28 AM
Last Post: Daniel
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 23,399 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 3,182 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 3,240 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 24,424 08/28/2016, 08:52 PM
Last Post: sheldonison
  Taylor polynomial. System of equations for the coefficients. marraco 17 28,358 08/23/2016, 11:25 AM
Last Post: Gottfried
  Tetration series for integer exponent. Can you find the pattern? marraco 20 29,014 02/21/2016, 03:27 PM
Last Post: marraco
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 64,041 03/27/2015, 11:28 PM
Last Post: tommy1729
  [integral] How to integrate a fourier series ? tommy1729 1 4,631 05/04/2014, 03:19 PM
Last Post: tommy1729
  Iteration series: Series of powertowers - "T- geometric series" Gottfried 10 24,523 02/04/2012, 05:02 AM
Last Post: Kouznetsov



Users browsing this thread: 1 Guest(s)