funcions cicle y transformada integral

(1/2)·( e^{(1/2)·pi·i}·e^{e^{(1/2)·pi·i}·x}+e^{(-1)·(1/2)·pi·i}·e^{e^{(-1)·(1/2)·pi·i}·x} )

(1/2)·( (-1)·e^{e^{(1/2)·pi·i}·x}+(-1)·e^{e^{(-1)·(1/2)·pi·i}·x} )

sin(x) = ...

... (1/2)·( ( e^{(1/2)·pi·i}/(p+e^{(1/2)·pi·i}) )+( e^{(-1)·(1/2)·pi·i}/(p+e^{(-1)·(1/2)·pi·i}) ) )

cos(x) = ...

... (1/2)·( ( e^{(2/2)·pi·i}/(p+e^{(1/2)·pi·i}) )+( e^{(-1)·(2/2)·pi·i}/(p+e^{(-1)·(1/2)·pi·i}) ) )

sin(x) = ( 1/(p^{2}+1) )

cos(x) = ( p/(p^{2}+1) )

e^{(1/3)·pi·i}·e^{e^{(1/3)·pi·i}·x}+e^{(-1)·(1/3)·pi·i}·e^{e^{(-1)·(1/3)·pi·i}·x}

e^{(2/3)·pi·i}·e^{e^{(1/3)·pi·i}·x}+e^{(-1)·(2/3)·pi·i}·e^{e^{(-1)·(1/3)·pi·i}·x}

(-1)·e^{e^{(1/3)·pi·i}·x}+(-1)·e^{e^{(-1)·(1/3)·pi·i}·x}

Rotx(x) = ...

... ( e^{(1/3)·pi·i}/(p+e^{(1/3)·pi·i}) )+( e^{(-1)·(1/3)·pi·i}/(p+e^{(-1)·(1/3)·pi·i}) )

Blau(x) = ...

... ( e^{(2/3)·pi·i}/(p+e^{(1/3)·pi·i}) )+( e^{(-1)·(2/3)·pi·i}/(p+e^{(-1)·(1/3)·pi·i}) )

Groc(x) = ...

... ( e^{(3/3)·pi·i}/(p+e^{(1/3)·pi·i}) )+( e^{(-1)·(3/3)·pi·i}/(p+e^{(-1)·(1/3)·pi·i}) )

Rotx(x) = ( (2+p)/(p^{2}+p+1) )

Blau(x) = ( (1+(-p))/(p^{2}+p+1) )

Groc(x) = ( ((-1)+(-2)·p)/(p^{2}+p+1) )

Rotx(ax) = ( (2a+p)/(p^{2}+ap+a^{2}) )

Blau(ax) = ( (a+(-p))/(p^{2}+ap+a^{2}) )

Groc(ax) = ( ((-a)+(-2)·p)/(p^{2}+ap+a^{2}) )

Rotx(ax)+Blau(ax) = 2·Rotx(ax)+Groc(ax) = 2·Blau(ax)+(-1)·Groc(ax)

Triangle equiláter de costat 1:

cos((1/3)·pi) = (1/2)

( (4+p)/(p^{2}+2p+4) ) = Rotx(2x)

( (2+(-p))/(p^{2}+2p+4) ) = Blau(2x)

( ((-2)+(-2)·p)/(p^{2}+2p+4) ) = Groc(2x)