integrals circulars

int[ z = e^{ix}+a ][ (z+a)^{2}(z+(-a))^{q} ] d_{x}[z] d[x] = ...

... int[ z = e^{ix}+a ][ (e^{ix}+2a)^{2}e^{qix} ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+a ][ (e^{2ix}+4ae^{ix}+4a^{2})e^{qix} ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+a ][ ie^{(q+3)ix}+4iae^{(q+2)ix}+4ia^{2}e^{(q+1)ix} ] d[x] = ...

... (1/(q+3))·e^{(q+3)ix}+4a·(1/(q+2))·e^{(q+2)ix}+4a^{2}·(1/(q+1))·e^{(q+1)ix}

int[ z = e^{ix}+(-a) ][ (z+a)^{p}(z+(-a))^{2} ] d_{x}[z] d[x] = ...

... int[ z = e^{ix}+(-a) ][ e^{pix}(e^{ix}+(-2)a)^{2} ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+(-a) ][ e^{pix}(e^{2ix}+(-4)ae^{ix}+4a^{2}) ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+(-a) ][ ie^{(p+3)ix}+(-4)iae^{(p+2)ix}+4ia^{2}e^{(p+1)ix} ] d[x] = ...

... (1/(p+3))·e^{(p+3)ix}+(-4)·a·(1/(p+2))·e^{(p+2)ix}+4a^{2}·(1/(p+1))·e^{(p+1)ix}

parells desordenats

No feu destructor en aquets teoremes perque és la valoració del pensament.

Energía de elipsoide-esfera-inscrita de paraula entitat.

El parell singletó es indestructible, de luz y de tiniebla.

{x,y} = {x}[ || ]{y}

z€{x,y}

z = x || z = y

z€{x} || z€{y}

z€{x}[ || ]{y}

}x,y{ = }x{[ & ]}y{

z€}x,y{

z != x & z != y

z€}x{ & z€}y{

z€}x{[ & ]}y{

Energía de camp de singletó de paraula de nucli indestructible.

x = y <==> {x}={y}

x = y

{x}={y}

}{x}{=}{y}{

x = y

x = y <==> }x{=}y{

x = y

}x{=}y{

{}x{}={}y{}

x = y

energía del camp elipsoide-esfera-inscrita

x el constructor.

y el destructor.

z el dual || el bi-tres-u.

{x,z,y} = {x}[ || ]{z}[ || ]{y}

t€{x,z,y}

t = x || t = z || t = y

t€{x} || t€{z} || t€{y}

t€{x}[ || ]{z}[ || ]{y}

}x,z,y{ = }x{[ & ]}z{[ & ]}y{

t€}x,z,y{

t != x & t != z & t != y

t€}x{ & t€}z{ & t€}y{

t€}x{[ & ]}z{[ & ]}y{

integral de residu imperial

lim[ a --> 0 ][ int[ 0-->2pi ][ z = ae^{ix} ][ f(z)/z^{(1/m)} ] d_{x}^{(1/m)}[z] d[x] ] = ...

... (2pi)·i^{(1/m)}·f(0)

d_{x}^{(1/m)}[x] = x^{(1/m)+(-1)·(1/m)} = x^{0} = 1

lim[ a --> 0 ][ int[ 0-->2pi ][ z = ae^{ix} ][ f(z)/z ] d_{x}[z] d[x] ] = 2pi·i·f(0) 

lim[ a --> 0 ][ int[ 0-->2pi ][ z = g^{o(-1)}(ae^{ix}) ][ f(z)/( g(z) )^{(1/m)} ] d_{x}^{(1/m)}[z] d[x] ] = ...

...  (2pi)·i^{(1/m)}·f( g^{o(-1)}(0) )·d_{0}^{(1/m)}[g^{o(-1)}(0)]

lim[ a --> 0 ][ int[ 0-->2pi ][ z = g^{o(-1)}(ae^{ix}) ][ f(z)/g(z) ] d_{x}[z] d[x] ] = ...

...  2pi·i·f( g^{o(-1)}(0) )·d_{0}[g^{o(-1)}(0)]

lim[ a --> 0 ][ int[ 0-->2pi ][ z = e^{ae^{ix}} ][ f(z)/ln(z) ] d_{x}[z] d[x] ] = ...

...  2pi·i·f(1)

lim[ a --> 0 ][ int[ 0-->2pi ][ z = ln(ae^{ix}) ][ f(z)/e^{z} ] d_{x}[z] d[x] ] = ...

...  2pi·i·f( ln(0) )·oo

lim[ a --> 0 ][ int[ 0-->2pi ][ z = e^{ae^{ix}} ][ f(z)/( ln(z) )^{(1/m)} ] d_{x}^{(1/m)}[z] d[x] ] = ...

...  2pi·i^{(1/m)}·f(1)

lim[ a --> 0 ][ int[ 0-->2pi ][ z = ln(ae^{ix}) ][ f(z)/( e^{z} )^{1/m} ] d_{x}^{(1/m)}[z] d[x] ] = ...

...  2pi·i^{(1/m)}·f( ln(0) )·oo^{(1/m)}

lim[ a --> 0 ][ int[ 0-->2pi ][ z = (ae^{ix})^{(1/n)} ][ f(z)/z^{n} ] d_{x}[z] d[x] ] = ...

...  2pi·i·f( 0^{(1/n)} )·(1/n)·0^{(1/n)}·oo

lim[ a --> 0 ][ int[ 0-->2pi ][ z = (ae^{ix})^{n} ][ f(z)/z^{(1/n)} ] d_{x}[z] d[x] ] = ...

...  2pi·i·f( 0^{n} )·n·0^{n}·oo

lim[ a --> 0 ][ int[ 0-->2pi ][ z = (ae^{ix})^{(1/n)} ][ f(z)/( z^{n} )^{(1/m)} ] d_{x}^{(1/m)}[z] d[x] ] = ...

...  2pi·i^{(1/m)}·f( 0^{(1/n)} )·(1/n^{(1/m)})·0^{(1/m)·(1/n)}·oo^{(1/m)}

lim[ a --> 0 ][ int[ 0-->2pi ][ z = (ae^{ix})^{n} ][ f(z)/( z^{(1/n)} )^{(1/m)} ] d_{x}^{(1/m)}[z] d[x] ] = ...

...  2pi·i^{(1/m)}·f( 0^{n} )·n^{(1/m)}·0^{(1/m)·n}·oo^{(1/m)}

destructor anti destrucció de centre

e^{ix} = sum[ (-1)^{k}·(1/(2k)!)·x^{2k} ]+i·sum[ (-1)^{k}·(1/(2k+1)!)·x^{(2k+1)} ]

e^{ix} = cos(x)+i·sin(x)

e^{ix} = (-1)·( cos(x)+i·sin(x) )

e^{ix} = (-1)·cos(x)+(-i)·sin(x)

e^{i(x/m)} = sum[ (-1)^{k}·(1/(2k)!)·(x/m)^{2k} ]+i·sum[ (-1)^{k}·(1/(2k+1)!)·(x/m)^{(2k+1)} ]

e^{i(x/m)} = cos(x/m)+i·sin(x/m)

e^{i(x/m)} = (-1)·( cos(x/m)+i·sin(x/m) )

e^{i(x/m)} = (-1)·cos(x/m)+(-i)·sin(x/m)

funcions neutre-expansives

Si f(x) = max{z€A: x [< z+x } ==> 0 [< f(x)

x [< z+x [< max{z€A: x [< z+x }+x = f(x)+x

Si f(x) = min{z€A: x >] z+x } ==> 0 >] f(x)

Si f(x) = max{z€A: 0 < x & x [< z·x } ==> 1 [< f(x)

x [< z·x [< max{z€A: x [< z·x }·x = f(x)·x

Si f(x) = min{z€A: 0 < x & x >] z·x } ==> 1 >] f(x)

Si f(x) = min{z€A: 0 > x & x [< z·x } ==> 1 [< f(x)

x [< z·x [< min{z€A: x [< z·x }·x = f(x)·x

Si f(x) = max{z€A: 0 > x & x >] z·x } ==> 1 >] f(x)

transitiu tenebrós

Si x < y_{n} & y_{n} < y_{n+1} ==> x < y_{n+1}

min{(0.n),(0.1)} < (0.(n+1))

Si z > y_{n} & y_{n} > y_{n+(-1)} ==> z > y_{n+(-1)}

min{1+(-1)·(0.n),(0.1)} < 1+(-1)·(0.(n+(-1)))

Si x = x & x < y_{n} ==> x < y_{n}

min{0,(0.n)} < (0.n)

Si z = z & z > y_{n} ==> z > y_{n}

min{0,1+(-1)·(0.n)} < 1+(-1)·(0.n)

Si y_{n} = y_{n} & y_{n} < y_{n+1} ==> y_{n} < y_{n+1}

min{0,(0.1)} < (0.1)

Si y_{n} = y_{n} & y_{n} > y_{n+(-1)} ==> y_{n} > y_{n+(-1)}

min{0,(0.1)} < (0.1)

Si f(y_{n}) = max{1,y_{n}} ==> y_{n} [< f(y_{n})

(0.n) [< 1

Si f(y_{n}) = min{0,y_{n}} ==> y_{n} >] f(y_{n})

Si f(y_{n}) = sup{1,y_{n}} ==> y_{n} < f(y_{n})

(0.n) < 1+s

Si f(y_{n}) = inf{0,y_{n}} ==> y_{n} > f(y_{n})

(0,(0.n)]_{A} [ |=| ] [(0.n),1)_{A} = (0,1)_{A}

0 < x [< (0.n) |=| (0.n) [< y < 1

[0,(0.n))_{A} [ |=| ] ((0.n),1]_{A} = [0,1]_{A}

integrals circulars imperials

2·int[ z = e^{ix}+p ][ (z+p)·(z+(-p)) ] d_{z}^{(1/m)}[z] d[x]

2·int[ (e^{ix}+2p)·e^{ix} i^{(1/m)}·e^{(i/m)·x} ] d[x]

2i^{(1/m)}·int[ e^{(2i+(i/m))·x}+2p·e^{(i+(i/m))·x} ] d[x]

2i^{(1/m)}·( (1/m^{(1/m)})·(1/(2i+(i/m))^{(1/m)})·e^{m·(2i+(i/m))·x}+...

... 2p·(1/m^{(1/m)})·(1/(i+(i/m))^{(1/m)})·e^{m·(i+(i/m))·x} )

2·(1/m^{(1/m)})·( (1/(2+(1/m))^{(1/m)})·e^{m·(2+(1/m))·i·x}+...

... 2p·(1/(1+(1/m))^{(1/m)})·e^{m·(1+(1/m))·i·x} )