Hmm, couldn't resist....
I just tried this for some numerical data without further checking, whether this all can eventually give a meaningful concept.
Anyway.
I've considered the ten fractionally indexed oprations between mul() and pow(). Base is sqrt(2), initial value x0 is 2.0 because with x0=1 the power-operation would give trivial result. The iteration-height h is 1,2 and 3. The (fractional) operation-index is k; k=0 means mul(x0,sqrt(2),h), k=1 means pow(x0,sqrt(2),h)
Here are the results:
Gottfried
I just tried this for some numerical data without further checking, whether this all can eventually give a meaningful concept.
Anyway.
I've considered the ten fractionally indexed oprations between mul() and pow(). Base is sqrt(2), initial value x0 is 2.0 because with x0=1 the power-operation would give trivial result. The iteration-height h is 1,2 and 3. The (fractional) operation-index is k; k=0 means mul(x0,sqrt(2),h), k=1 means pow(x0,sqrt(2),h)
Here are the results:
Code:
´ h=1 h=2 h=3
´ | 2.0* b^1.0 2.0* b^2.0 2.0* b^3.0
k | 2.82842712475 4.00000000000 5.65685424949 <--- mul(2,sqrt(2),h) , direct computation
-----------------------------------------------------
0.0 2.82842712475 4.00000000000 5.65685424949 = mul()
0.1 2.81156857833 4.00000000000 5.75322682321
0.2 2.79480389679 4.00000000000 5.85853861394
0.3 2.77814247936 4.00000000000 5.97272443872
0.4 2.76159351333 4.00000000000 6.09569942066
0.5 2.74516595391 4.00000000000 6.22787081195
0.6 2.72886850525 4.00000000000 6.37054764165
0.7 2.71270960247 4.00000000000 6.52607412279
0.8 2.69669739492 4.00000000000 6.69762735731
0.9 2.68083973075 4.00000000000 6.88877250162
1.0 2.66514414269 4.00000000000 7.10299330132 = pow()
-----------------------------------------------------
| 2.66514414269 4.00000000000 7.10299330132 <--- pow(2,sqrt(2),h) , direct computation
| 2.0^ b^1.0 2.0^ b^2.0 2.0^ b^3.0Gottfried
Gottfried Helms, Kassel
