The Hot Pepper

POTAWIE'S CLUB ROYALE got my vote, meaty goodness!

Oh you know.....a bit of this and a bit of that!!

Oh yeah and I broke up with my girlfriend! nothing to exciting really...

I reckon we call him cricket.

Should be Madge.

THP,

I love the fourier series as the functions are simply mind boggli ng.


The fourier series of the function f(x)

a(0) / 2 + (k=1..) (a(k) cos kx + b(k) sin kx)
a(k) = 1/PI f(x) cos kx dx
b(k) = 1/PI f(x) sin kx dx
Remainder of fourier series. Sn(x) = sum of first n+1 terms at x.

remainder(n) = f(x) - Sn(x) = 1/PI f(x+t) Dn(t) dt

Sn(x) = 1/PI f(x+t) Dn(t) dt
Dn(x) = Dirichlet kernel = 1/2 + cos x + cos 2x + .. + cos nx = [ sin(n + 1/2)x ] / [ 2sin(x/2) ]
Riemann's Theorem. If f(x) is continuous except for a finite # of finite jumps in every finite interval then:

lim(k->) f(t) cos kt dt = lim(k->)f(t) sin kt dt = 0

The fourier series of the function f(x) in an arbitrary interval.

A(0) / 2 + (k=1..) [ A(k) cos (k(PI)x / m) + B(k) (sin k(PI)x / m) ]
a(k) = 1/m f(x) cos (k(PI)x / m) dx
b(k) = 1/m f(x) sin (k(PI)x / m) dx
Parseval's Theorem. If f(x) is continuous; f(-PI) = f(PI) then

1/PI f^2(x) dx = a(0)^2 / 2 + (k=1..) (a(k)^2 + b(k)^2)

Fourier Integral of the function f(x)

f(x) = ( a(y) cos yx + b(y) sin yx ) dy
a(y) = 1/PI f(t) cos ty dt
b(y) = 1/PI f(t) sin ty dt

Special Cases of Fourier Integral

if f(x) = f(-x) then

f(x) = 2/PI cos xy dy f(t) cos yt dt
if f(-x) = -f(x) then
f(x) = 2/PI sin xy dy sin yt dt
Fourier Transforms

Fourier Cosine Transform

g(x) = (2/PI)f(t) cos xt dt

Fourier Sine Transform

g(x) = (2/PI)f(t) sin xt dt

Identities of the Transforms

If f(-x) = f(x) then
Fourier Cosine Transform ( Fourier Cosine Transform (f(x)) ) = f(x)
If f(-x) = -f(x) then
Fourier Sine Transform (Fourier Sine Transform (f(x)) ) = f(x)

yeah actually I did...... I had to look twice cause I couldn't believe my eyes!!!

Oh my GOD........I bet you were pissing yourself laughing when you pressed the enter button to save that bloody pic on my page.....

thp,

Buddy you must have been dead drunk because you have sent this message.

We talk tomorrow. Take care.

NJA

glad you like the pic if you think its a bit on the possibly offensive side let me know and i'll change it thailand has it all big rocks, ladyboys and great food

You were just jealous of the huge photochopped manhood.

hmmmm, you just wanted me to bump up your home page counter didn't you...

You never fail to come up with something awesome! Do your 'thang NYC!!

But of course you will enter. It would truly be a FAIL were you to not, what with all the great deli style sammich's out of NYC. Get thee to thine deli of choice for thine meat and cheese products and go forth and beginneth thine bready creations!

Feel free to begin talking your Noo 'Yawk smack for the sammich t-down 'ya bum!!

Trouble is my name! What vintage of trouble would you wish to open? Choose on that goes well with cow!

oh really??? And here was me only saying nice things about the queen.....Well no more!!

I joined RF in the summer of 2004. That is how I found THP.