08/12/2007, 05:34 PM

In german pupils competition ("Jugend forscht") Markus Müller presented 1996(?) an article, called "Reihenalgebra", where he discussed higher operators like tetration, pentation and so on. Two aspects have been of special interest to me:

1) He started the index of operators differently:

1 - do nothing

2 - shift by 1

3 - addition

4 - multiplication

5 - exponentiation

6 - tetration

and so on.

Then he indexed the inverses like

1 - do nothing

1/2 - shift by -1

1/3 - subtraction

1/4 - division

and so on (considering also the different inverses of higher index)

2) Based on this he even tried to define operations of fractional order

The original article is a nice treatise, recalling that it was done by a pupil; unfortunately it is in windows write 3.11 format and not directly transferable to current word-/pdf-formats.

Recently I found an update of this concept

http://www.math.tu-berlin.de/~mueller/reihenalgebra.pdf

where Markus Müller seems to be affiliated to the TU of Berlin.

Possibly the administrator would like to invite Markus Müller to this forum (provided he is still interested in the subject). I would like to know, what he has to say about the current research.

Gottfried

1) He started the index of operators differently:

1 - do nothing

2 - shift by 1

3 - addition

4 - multiplication

5 - exponentiation

6 - tetration

and so on.

Then he indexed the inverses like

1 - do nothing

1/2 - shift by -1

1/3 - subtraction

1/4 - division

and so on (considering also the different inverses of higher index)

2) Based on this he even tried to define operations of fractional order

The original article is a nice treatise, recalling that it was done by a pupil; unfortunately it is in windows write 3.11 format and not directly transferable to current word-/pdf-formats.

Recently I found an update of this concept

http://www.math.tu-berlin.de/~mueller/reihenalgebra.pdf

where Markus Müller seems to be affiliated to the TU of Berlin.

Possibly the administrator would like to invite Markus Müller to this forum (provided he is still interested in the subject). I would like to know, what he has to say about the current research.

Gottfried

Gottfried Helms, Kassel