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