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correct derivatives wrt iteration height?
#1
Hi
I never followed the discussions about derivatives/integrals (it was all much enough with that what I had to follow... :-) )
Now I'm trying to step into that field, first trying to re-express the derivatives wrt to the height-parameter in terms of my matrix-language.
Could someone crosscheck, whether these values match the "official" values?
Code:
Table of derivatives wrt iteration-height h of f°h(x):  df°h(x)/dh
          using f(x) = 2^x - 1
          First derivatives at few different heights and x.
          At h=0 I have also computed the second derivatives.
------------------------------------------------------------------
         h=0.1        h=0             h=-0.5          h=-1
------------------------------------------------------------------
x=1.5    0.2478643    0.2332798       0.17517130      0.13462
                      0.13462
------------------------------------------------------------------
x=1      0            0               0               0
                      0
------------------------------------------------------------------
x=0.5    0.0862732    0.0862134       0.08516093     -0.08291
                     -0.08291
------------------------------------------------------------------
x=0      0            0               0               0
                      0
------------------------------------------------------------------
x=-0.5   0.2715139    0.2945423       0.46660375      0.849869
                     -0.244133
------------------------------------------------------------------
x=-1     0.7414847    0.8498694       2.14011104      ???
                     -1.205064
------------------------------------------------------------------
x=-2     2.3070256    3.0900585       ???             ???
                    -10.03082
------------------------------------------------------------------
Do the values match -for instance- the Kuznetsov-derivatives?

Gottfried
Gottfried Helms, Kassel
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