06/23/2010, 04:26 PM

an intresting paper related to continuum sum ( but not continuum iterations of it ) is this :

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

especially " 3. Basic Algebraic Identities " where the geometric part is what mike3 uses (together with fourrier expansion) to get his continuum sum.

the idea of ' removing the period ' is also known and the origin of this 'geometric part equation' is as old as " q-math " ( q-series and q-analogues and fourrier series )

i knew id seen it before ... in fact i used it myself even way before that paper was written , although probably similar papers have been written much earlier.

not to mention eulers example given in the paper.

intresting is the continuum product

product x ; sin(x) + 5/4.

or equivalent the continuum sum

sum x ; ln(sin(x) + 5/4).

and the question if these sums resp products are periodic themselves.

and the question if these sums resp products are divergent ( lim x -> oo does not equal +/-oo or 0)

( it is known that integral 0,2pi log(sin(x) + 5/4) = 0 )

regards

tommy1729

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

especially " 3. Basic Algebraic Identities " where the geometric part is what mike3 uses (together with fourrier expansion) to get his continuum sum.

the idea of ' removing the period ' is also known and the origin of this 'geometric part equation' is as old as " q-math " ( q-series and q-analogues and fourrier series )

i knew id seen it before ... in fact i used it myself even way before that paper was written , although probably similar papers have been written much earlier.

not to mention eulers example given in the paper.

intresting is the continuum product

product x ; sin(x) + 5/4.

or equivalent the continuum sum

sum x ; ln(sin(x) + 5/4).

and the question if these sums resp products are periodic themselves.

and the question if these sums resp products are divergent ( lim x -> oo does not equal +/-oo or 0)

( it is known that integral 0,2pi log(sin(x) + 5/4) = 0 )

regards

tommy1729