@henryk - well, take your time 
@andrew - yes, i think you got this right.
@all...
well, if the multiplicative coefficient to the schröder-function, which is of the form b^h, would be consistent, I would have made "a thing of it". But since their forms for the three operations are not constant and also not "linear" (in some sense) I doubt this all is eventually much helpful.
Just try to continue that sequence to higher integer indexes.. it looks to me as some well known try to extend the sequence of operations with some symmetric approach, as Andy has referred to.
So my first impression was, that this all might be -besides its nice appeal from the fractional indexes between mul() and pow() - somehow trivial.
Actually, if I don't get an intriguing and practicable idea how to "linearize" the structure of the cofactor of the schröder-function, then I feel this all as somehow "suboptimal" (though extremely interesting & animating...). But may be, my notorious trend to perfectionisnm keeps me away from recognizing some present useful aspect...
You see: I'm not having the feeling of a proper standing here...
<G>
[... including some updating...]
@andrew - yes, i think you got this right.
@all...
well, if the multiplicative coefficient to the schröder-function, which is of the form b^h, would be consistent, I would have made "a thing of it". But since their forms for the three operations are not constant and also not "linear" (in some sense) I doubt this all is eventually much helpful.
Just try to continue that sequence to higher integer indexes.. it looks to me as some well known try to extend the sequence of operations with some symmetric approach, as Andy has referred to.
So my first impression was, that this all might be -besides its nice appeal from the fractional indexes between mul() and pow() - somehow trivial.
Actually, if I don't get an intriguing and practicable idea how to "linearize" the structure of the cofactor of the schröder-function, then I feel this all as somehow "suboptimal" (though extremely interesting & animating...). But may be, my notorious trend to perfectionisnm keeps me away from recognizing some present useful aspect...
You see: I'm not having the feeling of a proper standing here...
<G>
[... including some updating...]
Gottfried Helms, Kassel
