Tetration: Fractional iteration of a complex base Gottfried Helms, Jul 2008
Iteration by exponential polynomial interpolation (by FP-shift) Integer iteration
h Uth(x) Error (by EulerSum) Tbh(x") Uth(x) Tbh(x")
  real imag real imag real imag real imag real imag real imag                            
-3 0 -0.324904 -0.093644 1.55E-21 -4.36E-22 0.703518 0.980940 -0.324904 -0.093644 0.703518 0.980940
-2.9 0 -0.317357 -0.124172 -2.59E-21 -6.76E-21 0.757592 0.967595
-2.8 0 -0.307616 -0.153982 -8.68E-21 -2.24E-20 0.812350 0.958278
-2.7 0 -0.295768 -0.183045 3.97E-21 -5.10E-20 0.867675 0.952882
-2.6 0 -0.281872 -0.211338 4.99E-20 -5.76E-20 0.923483 0.951330
-2.5 0 -0.265960 -0.238846 8.17E-20 -1.27E-20 0.979722 0.953586
-2.4 0 -0.248037 -0.265549 5.78E-20 3.33E-20 1.036357 0.959658
-2.3 0 -0.228083 -0.291419 1.91E-20 3.59E-20 1.093363 0.969601
-2.2 0 -0.206053 -0.316419 3.04E-21 1.92E-20 1.150716 0.983514
-2.1 0 -0.181883 -0.340493 9.95E-22 7.95E-21 1.208384 1.001546
-2 0 -0.155487 -0.363568 1.30E-22 2.73E-21 1.266320 1.023890 -0.155487 -0.363568 1.266320 1.023890
-1.9 0 -0.126762 -0.385548 -3.95E-21 -1.72E-21 1.324461 1.050788
-1.8 0 -0.095585 -0.406312 -1.11E-20 -1.33E-20 1.382717 1.082532
-1.7 0 -0.061815 -0.425708 -7.39E-21 -3.96E-20 1.440969 1.119469
-1.6 0 -0.025289 -0.443547 2.98E-20 -5.99E-20 1.499054 1.162010
-1.5 0 0.014178 -0.459593 7.61E-20 -3.13E-20 1.556752 1.210638
-1.4 0 0.056785 -0.473550 7.14E-20 2.43E-20 1.613766 1.265912
-1.3 0 0.102747 -0.485049 2.97E-20 4.26E-20 1.669693 1.328472
-1.2 0 0.152283 -0.493630 4.36E-21 2.77E-20 1.723995 1.399039
-1.1 0 0.205602 -0.498732 -1.10E-21 1.34E-20 1.775964 1.478406
-1 0 0.262893 -0.499669 -3.47E-21 6.59E-21 1.824679 1.567432 0.262893 -0.499669 1.824679 1.567432
-0.9 0 0.324297 -0.495614 -1.07E-20 1.21E-21 1.868961 1.667024
-0.8 0 0.389887 -0.485575 -2.51E-20 -1.37E-20 1.907316 1.778110
-0.7 0 0.459623 -0.468369 -3.16E-20 -5.55E-20 1.937857 1.901606
-0.6 0 0.533304 -0.442597 1.57E-20 -1.11E-19 1.958224 2.038350
-0.5 0 0.610487 -0.406615 1.17E-19 -9.41E-20 1.965474 2.189002
-0.4 0 0.690379 -0.358521 1.50E-19 1.77E-20 1.955976 2.353890
-0.3 0 0.771698 -0.296168 7.00E-20 9.36E-20 1.925304 2.532774
-0.2 0 0.852491 -0.217213 -1.63E-20 7.81E-20 1.868176 2.724523
-0.1 0 0.929914 -0.119243 -6.72E-20 3.93E-20 1.778464 2.926672
0 0 1.000000 0.000000 -1.32E-19 0.00E+00 1.649357 3.134864 1.000000 0.000000 1.649357 3.134864
0.1 0 1.057429 0.142253 -2.65E-19 -9.87E-20 1.473745 3.342193
0.2 0 1.095362 0.308181 -4.75E-19 -4.36E-19 1.244948 3.538487
0.3 0 1.105444 0.496601 -4.95E-19 -1.44E-18 0.957927 3.709677
0.4 0 1.078126 0.703496 1.12E-18 -3.48E-18 0.611103 3.837479
0.5 0 1.003521 0.920893 7.98E-18 -4.00E-18 0.208823 3.899824
0.6 0 0.873057 1.135869 1.99E-17 1.01E-17 -0.235728 3.872616
0.7 0 0.682054 1.330217 2.19E-18 5.71E-17 -0.697871 3.733506
0.8 0 0.433054 1.481546 -1.38E-16 6.01E-17 -1.140414 3.468013
0.9 0 0.139018 1.566654 -2.36E-16 -3.23E-16 -1.516300 3.077320
1 0 -0.175321 1.567432 8.37E-16 -6.58E-16 -1.776749 2.585255 -0.175321 1.567432 -1.776749 2.585255
1.1 0 -0.476116 1.478056 1.34E-15 2.47E-15 -1.884717 2.040073
1.2 0 -0.728161 1.310275 -7.24E-15 7.47E-16 -1.829588 1.506645
1.3 0 -0.905898 1.092716 9.23E-15 -1.60E-14 -1.635154 1.048638
1.4 0 -1.002312 0.862394 8.77E-15 4.55E-14 -1.353651 0.707575
1.5 0 -1.029938 0.651856 -7.43E-14 -9.01E-14 -1.046429 0.490646
1.6 0 -1.012962 0.479322 2.54E-13 1.62E-13 -0.761993 0.374969
1.7 0 -0.975867 0.347233 -7.63E-13 -2.97E-13 -0.524362 0.324181
1.8 0 -0.935787 0.247943 2.20E-12 4.19E-13 -0.335679 0.305122
1.9 0 -0.901205 0.170871 -5.52E-12 5.25E-14 -0.186356 0.295768
2 0 -0.874559 0.106843 1.13E-11 -2.07E-12 -0.064020 0.284732 -0.874559 0.106843 -0.064020 0.284732
2.1 0 -0.855238 0.049198 -1.91E-11 5.46E-12 0.042267 0.267478
2.2 0 -0.841291 -0.006691 6.23E-14 -6.41E-15 0.141371 0.243247
2.3 0 -0.829859 -0.063964 -1.91E-13 -2.65E-13 0.240571 0.213935
2.4 0 -0.817161 -0.124018 -8.58E-13 1.11E-12 0.345174 0.184313
2.5 0 -0.799308 -0.185608 4.42E-12 3.16E-12 0.456434 0.161504
2.6 0 -0.774462 -0.244910 1.53E-11 -1.44E-11 0.569876 0.151544
2.7 0 -0.744406 -0.297943 -3.51E-11 -8.32E-11 0.677787 0.154919
2.8 0 -0.713205 -0.343391 -1.51016E-09 1.29E-10 0.774755 0.166344
2.9 0 -0.684407 -0.382891 3.68977E-09 3.40397E-09 0.860419 0.178909
3 0 -0.659676 -0.419391 1.23111E-09 -1.43292E-08 0.938025 0.187571 -0.659676 -0.419391 0.938025 0.187571