08/05/2014, 11:16 PM
Some Top posters of the tetration forum :
Bo " administrator " 198214
Tommy " sinh " 1729
Gottfried " matrix " Helms
Jay "excel" fox
sheldon " theta wave "
mike "continuum sum " 3
Jms " transform " Nxn
Ive been wanting to post that silly thing for a long time
Anyway the posts made by Gottfried and Jay look familiar to me.
I also used excel to accelerate the computation of the sequence and investigate its number theoretic properties.
I Always factor number sequences.
Anyways a few remarks/ideas :
1) Many years ago I mentioned the equations
A) f ' (2x) = 3 f(x) + C
B) f ' (x) = f(x/2) + f(x/3) + C
at , if im not mistaken , sci.math.
Seeing Jay's f ' (2x) = f(x) makes me wonder about those again.
Unfortunately I have holes in my brain.
2) Our sequence satisfies f(n) - f(n-1) - (f(n-1) - f(n-2)) = f(n-2) or similar if we IGNORE ZERO. I havent quite made that clear before.
3) What I was really looking for is a closed form expression for the sequence.
Some transformation or such like for the gamma function.
4) I would like a single functional equation for the series that is exact and does NOT use rounding. If possible.
5) I would like to comment that f(x) - f(x-1) can Always be approximated by
f(x) - ( f(x) - f ' (x) + f '' (x)/2 - f "' (x)/6 + f ""(x)/24 )
Hence differences / difference equations can be approximated by differential / differential equations.
This might be usefull as it has been in the past.
Maybe it can connect Jay's f(x) with the Original sequence , maybe express one in terms of the other or solve 3) or 4).
Those are the most important things for me.
regards
tommy1729
Bo " administrator " 198214
Tommy " sinh " 1729
Gottfried " matrix " Helms
Jay "excel" fox
sheldon " theta wave "
mike "continuum sum " 3
Jms " transform " Nxn
Ive been wanting to post that silly thing for a long time
Anyway the posts made by Gottfried and Jay look familiar to me.
I also used excel to accelerate the computation of the sequence and investigate its number theoretic properties.
I Always factor number sequences.
Anyways a few remarks/ideas :
1) Many years ago I mentioned the equations
A) f ' (2x) = 3 f(x) + C
B) f ' (x) = f(x/2) + f(x/3) + C
at , if im not mistaken , sci.math.
Seeing Jay's f ' (2x) = f(x) makes me wonder about those again.
Unfortunately I have holes in my brain.
2) Our sequence satisfies f(n) - f(n-1) - (f(n-1) - f(n-2)) = f(n-2) or similar if we IGNORE ZERO. I havent quite made that clear before.
3) What I was really looking for is a closed form expression for the sequence.
Some transformation or such like for the gamma function.
4) I would like a single functional equation for the series that is exact and does NOT use rounding. If possible.
5) I would like to comment that f(x) - f(x-1) can Always be approximated by
f(x) - ( f(x) - f ' (x) + f '' (x)/2 - f "' (x)/6 + f ""(x)/24 )
Hence differences / difference equations can be approximated by differential / differential equations.
This might be usefull as it has been in the past.
Maybe it can connect Jay's f(x) with the Original sequence , maybe express one in terms of the other or solve 3) or 4).
Those are the most important things for me.
regards
tommy1729