Hi everyone. My name is Lucas Gryglicki.

I was born in 16th July 1982.

I will have some questions for You, I'm browsing this forum since some years, and I'm a big fan of math and specially tetration is my main interest. I've written many program with successfull linear, quadric approx, but currently got stuck in analytical formula for any base.

I will ask for it later.

Hello to all of You.

My problem is:

From this forum: analytical formula for tetration:

http://math.eretrandre.org/tetrationforu...hp?tid=576

sum(0...inf) A_n * L^(Nz)

This seems to be for base E only, but I found formula for A_n for any base

I have algorithm to find L for b

I have algorithm to compute A_n -- bell complete of recursive previous A_n-1 with log(b) terms etc - it works and gives correct results, but when I finally try it even for base E and for z = -1,0,1,2 I should get 0,1,E,E^E but I get strange things .... Henryk told me that this formula has singularities in integer values, but this is new info for me, I was trying many many days to understand why it fails.

So is there *any* formula to compute sexp(z) for any base E - some infinite sum

I tried A_n * (z-L)^N, etc - nothing helps....

Maybe I'm totally wrong with some key properties of this formula?

If Anyone of You wants then please take a look at attached anal.cc

It can be easily compiled with gcc

g++ -o anal anal.cc

Many other of my progs uses MPFR, MPC, GMP itd, OpenGL - but this one is the simplest one it contains: LUP decomposition, determinant of NxN matrix, factorials, binonmials compute, bell complete polynomial, recurence formula for A_n.... and finite sum of A_n * ?? --> to get some simplest tetrations for lets say b=2 and for z = 0; 0.5; 1 - but it fails and I don't know why

Prog is anal.cc inside ZIP with some other of my tetration attempts

mpctet.cc is linear and quadric approximation

newton.cc is Newton approx

render.cc is opengl renderer of results

There are binaries too for FreeBSD UNIX 10-CURRENT

I any of You want then You can remotely login to my home server through SSH

IP: 88.199.169.19

Port: 9922

Login and Pass with private msgs only

It is quite a powerful server, with ZFS mirror pools, 16 GB of RAM, 4 CPUs....

can do many many math computation quite fast.

I've made some programs to see how current results look like.

Written generic program to display

Base:

Br0 --> Br1, step Bri (iterate base in real direction)

Bi0 --> Bi1, step Bii (iterate base in imag direction)

Height:

Xr0 --> Xr1, step Xri (iterate tetration height in real direction)

Xr0 --> Xi1, step Xii (iterate tetration in imag direction)

Finally we have 4 ranges as input and output is complex value (Cr, Ci)

CSV is c = b^^x

br_idx;bi_idx;xr_idx;xi_idx;br;bi;xr;xi;cr;ci;

Lots of lines

New program render4.cc handles this, and anal.cc outputs to such a file.

Values are strange and I don't know how to fix it.

genexp.cc will generate such values for exponent b^x, this is for testing render4. New zip:tet.zip

Also anal handles perdiodic of b^^x to fins point which is nearest to L, and then iterate +/- 1,2,3.... in real direction to get as close as possible to L, and using b^^x = b^(b^^(x-1)) or b^^x = log(b^^(x+1))/log(b) during each step.

I was born in 16th July 1982.

I will have some questions for You, I'm browsing this forum since some years, and I'm a big fan of math and specially tetration is my main interest. I've written many program with successfull linear, quadric approx, but currently got stuck in analytical formula for any base.

I will ask for it later.

Hello to all of You.

My problem is:

From this forum: analytical formula for tetration:

http://math.eretrandre.org/tetrationforu...hp?tid=576

sum(0...inf) A_n * L^(Nz)

This seems to be for base E only, but I found formula for A_n for any base

I have algorithm to find L for b

I have algorithm to compute A_n -- bell complete of recursive previous A_n-1 with log(b) terms etc - it works and gives correct results, but when I finally try it even for base E and for z = -1,0,1,2 I should get 0,1,E,E^E but I get strange things .... Henryk told me that this formula has singularities in integer values, but this is new info for me, I was trying many many days to understand why it fails.

So is there *any* formula to compute sexp(z) for any base E - some infinite sum

I tried A_n * (z-L)^N, etc - nothing helps....

Maybe I'm totally wrong with some key properties of this formula?

If Anyone of You wants then please take a look at attached anal.cc

It can be easily compiled with gcc

g++ -o anal anal.cc

Many other of my progs uses MPFR, MPC, GMP itd, OpenGL - but this one is the simplest one it contains: LUP decomposition, determinant of NxN matrix, factorials, binonmials compute, bell complete polynomial, recurence formula for A_n.... and finite sum of A_n * ?? --> to get some simplest tetrations for lets say b=2 and for z = 0; 0.5; 1 - but it fails and I don't know why

Prog is anal.cc inside ZIP with some other of my tetration attempts

mpctet.cc is linear and quadric approximation

newton.cc is Newton approx

render.cc is opengl renderer of results

There are binaries too for FreeBSD UNIX 10-CURRENT

I any of You want then You can remotely login to my home server through SSH

IP: 88.199.169.19

Port: 9922

Login and Pass with private msgs only

It is quite a powerful server, with ZFS mirror pools, 16 GB of RAM, 4 CPUs....

can do many many math computation quite fast.

I've made some programs to see how current results look like.

Written generic program to display

Base:

Br0 --> Br1, step Bri (iterate base in real direction)

Bi0 --> Bi1, step Bii (iterate base in imag direction)

Height:

Xr0 --> Xr1, step Xri (iterate tetration height in real direction)

Xr0 --> Xi1, step Xii (iterate tetration in imag direction)

Finally we have 4 ranges as input and output is complex value (Cr, Ci)

CSV is c = b^^x

br_idx;bi_idx;xr_idx;xi_idx;br;bi;xr;xi;cr;ci;

Lots of lines

New program render4.cc handles this, and anal.cc outputs to such a file.

Values are strange and I don't know how to fix it.

genexp.cc will generate such values for exponent b^x, this is for testing render4. New zip:tet.zip

Also anal handles perdiodic of b^^x to fins point which is nearest to L, and then iterate +/- 1,2,3.... in real direction to get as close as possible to L, and using b^^x = b^(b^^(x-1)) or b^^x = log(b^^(x+1))/log(b) during each step.

Fuji GSW690III

Nikon D3, Nikkors 14-24/2.8, 24/1.4, 35/2, 50/1.4, 85/1.4, 135/2, 80-200/2.8

Nikon D3, Nikkors 14-24/2.8, 24/1.4, 35/2, 50/1.4, 85/1.4, 135/2, 80-200/2.8