Si d[x] = r·d[s] ==>
m·d_{tt}^{2}[x] = F·(s+1)^{p}·e^{s+1}
(m/r)·d_{t}[x]^{2} = F·(s+1)^{p+1}·er-h[p+1](s+1)+N
N = 0 <==> ...
... ( s+1 = Anti-pow[p+1]-er-h[p+1]( (2e)/(p+1) ) & d_{t}[x] = ( F·(r/m)·( (2e)/(p+1) ) )^{(1/2)} )
Deducción:
1^{k} = 1 = x^{0·k}
er-h[p+1](1) = er-h[p+1](x^{0}) = sum[k = 1]-[oo][ (1/k!)·( 1/(0·k+p+1) ) ] = ( e/(p+1) )
Ley:
Si d[x] = r·d[s] ==>
m·d_{tt}^{2}[x] = F·(s+1)^{p}·arc-tan(s+1)
(m/r)·d_{t}[x]^{2} = F·(s+1)^{p+1}·arc-tan-e[p+1](s+1)+N
N = 0 <==> ...
... ( s+1 = Anti-pow[p+1]-arc-tan-e[p+1]( (1/2)·( pi/(p+1) ) ) & ...
... d_{t}[x] = ( F·(r/m)·( (1/2)·( pi/(p+1) ) ) )^{(1/2)} )
Ley:
m·d_{tt}^{2}[x] = F·(ut+1)^{p}·e^{ut+1}
d_{t}[x(0)] = (F/m)·(1/u)·( e/(p+1) )
Ley:
m·d_{tt}^{2}[x] = F·(ut+1)^{p}·arc-tan(ut+1)
d_{t}[x(0)] = (F/m)·(1/u)·(1/4)·( pi/(p+1) )
Master en Física-Matemática:
Integración de funciones error en series de potencias
Mecánica-Matemática
Series de Fourier
Laplaciano-Físico:
d_{xx}^{2}[u(x,t)] = (1/v)^{2}·d_{tt}^{2}[u(x,t)]
Laplaciano-Cuántico-Físico:
d_{xx}^{2}[u(x,t)]+(1/h)^{2}·( mE )·u(x,t) = (1/v)^{2}·d_{tt}^{2}[u(x,t)]
Series de Garriga
Garriguense-Físico:
d_{x}[u(x,t)] [o] ( u(x,t) )^{[o] n} = (1/v)·d_{t}[u(x,t)]
Divergencia-Física:
d_{x}[u(x,t)] = (1/v)·d_{t}[u(x,t)]
Divergencia-Lineal-Física:
d_{x}[u(x,t)]+(1/r)·u(x,t) = (1/v)·d_{t}[u(x,t)]
Calor-Matemático:
d_{x}[u(x,t)] = (1/a)·d_{tt}^{2}[u(x,t)]
Calor-Lineal-Matemático:
d_{x}[u(x,t)]+(1/r)·u(x,t) = (1/a)·d_{tt}^{2}[u(x,t)]
Ecuación de Plank:
d_{xx}^{2}[u(x,t)] = (m/h)·d_{t}[u(x,t)]
Radiación cuántica de 2 electrones de des-enlace de spines opuestos.
Ecuación de Srödinguer:
p = 1+s
p = 3+s
p = 5+s
p = 7+s
d_{xx}^{2}[u(x,t)]+(1/h)^{2}·( m·E((2n+1),(r/a),s) )·u(x,t) = (m/h)·d_{t}[u(x,t)]
Serie de Fourier elíptica:
Teorema:
f(x)·cos(kx) = a_{k}·(cos(kx) )^{2}+b_{k}·sin(kx)·cos(kx)
f(x)·sin(kx) = a_{k}·cos(kx)·sin(kx)+b_{k}·( sin(kx) )^{2}
Teorema:
int[x = (-pi)]-[pi][ cos(kx)·cos(nx) ] = 0
int[x = (-pi)]-[pi][ cos(kx)·sin(nx) ] = 0
int[x = (-pi)]-[pi][ sin(kx)·cos(nx) ] = 0
int[x = (-pi)]-[pi][ sin(kx)·sin(nx) ] = 0
Demostración:
(1/(kn))·( ( sin(k·pi)·sin(n·pi)·x )+(-1)·( sin(k·pi)·sin(n·pi)·x ) ) = 0
(1/(kn))·( (-1)·( sin(k·pi)·cos(n·pi)·x )+(-1)·( sin(k·pi)·cos(n·pi)·x ) ) = 0
(1/(kn))·( (-1)·( cos(k·pi)·sin(n·pi)·x )+(-1)·( cos(k·pi)·sin(n·pi)·x ) ) = 0
(1/(kn))·( ( cos(k·pi)·cos(n·pi)·x )+(-1)·( cos(k·pi)·cos(n·pi) x ) ) = 0
Teorema:
int[x = (-pi)]-[pi][ ( cos(kx) )^{2} ] = pi
int[x = (-pi)]-[pi][ ( sin(kx) )^{2} ] = pi
Demostración:
int[x = (-pi)]-[pi][ ( cos(kx) )^{2}+( sin(kx) )^{2} ] = int[x = (-pi)]-[pi][ 1 ]d[x] = 2pi
Teorema:
f(x) = (1/(2pi))·int[x = (-pi)]-[pi][f(x)]d[x]+sum[k = 1]-[oo][ ...
... (1/pi)·int[x = (-pi)][pi][ f(x)·cos(kx) ]d[x]·cos(kx)+...
... (1/pi)·int[x = (-pi)][pi][ f(x)·sin(kx) ]d[x]·sin(kx)
... ]
Serie de Fourier hiperbólica:
Teorema:
f(x)·cosh(kx) = a_{k}·(cosh(kx) )^{2}+b_{k}·sinh(kx)·cosh(kx)
f(x)·sinh(kx) = a_{k}·cosh(kx)·sinh(kx)+b_{k}·( sinh(kx) )^{2}
Teorema:
int[x = (-pi)·i]-[pi·i][ cosh(kx)·cosh(nx) ] = 0
int[x = (-pi)·i]-[pi·i][ cosh(kx)·sinh(nx) ] = 0
int[x = (-pi)·i]-[pi·i][ sinh(kx)·cosh(nx) ] = 0
int[x = (-pi)·i]-[pi·i][ sinh(kx)·sinh(nx) ] = 0
Teorema:
int[x = (-pi)·i]-[pi·i][ ( cosh(kx) )^{2} ] = pi·i
int[x = (-pi)·i]-[pi·i][ (-1)·( sinh(kx) )^{2} ] = pi·i
Demostración:
int[x = (-pi)·i]-[pi·i][ ( cosh(kx) )^{2}+(-1)·( sinh(kx) )^{2} ] = int[x = (-pi)·i]-[pi·i][ 1 ]d[x] = 2pi·i
Teorema:
f(x) = (1/(2pi·i))·int[x = (-pi)·i]-[pi·i][f(x)]d[x]+sum[k = 1]-[oo][ ...
... (1/(pi·i))·int[x = (-pi)·i][pi·i][ f(x)·cosh(kx) ]d[x]·cosh(kx)+...
... (-1)·(1/(pi·i))·int[x = (-pi)·i][pi·i][ f(x)·sinh(kx) ]d[x]·sinh(kx)
... ]
Teorema: [ de serie de Fourier elíptica ]
[Ax][ x € R ]
x^{2} = (1/3)·pi^{2}+sum[k = 1]-[oo][ ( 4·(1/k)^{2}·cos(k·pi) )·cos(kx) ]
Teorema: [ de serie de Fourier hiperbólica ]
[Ax][ x € C ]
x^{2} = (-1)·(1/3)·pi^{2}+sum[k = 1]-[oo][ (-1)·( 4·(1/k)^{2}·cosh(k·pi·i) )·cosh(kx) ]
Teorema:
sum[k = 1]-[oo][ (1/k)^{2} ] = (1/6)·pi^{2}
sum[k = 1]-[oo][ (-1)^{k}·(1/k)^{2} ] = (-1)·(1/12)·pi^{2}
Teorema: [ de serie de Fourier elíptica ]
[Ax][ x € R ]
x^{4} = ...
... (1/5)·pi^{4}+sum[k = 1]-[oo][ ( ( 8pi^{2}·(1/k)^{2}+(-48)·(1/k)^{4} )·cos(k·pi) )·cos(kx) ]
Teorema: [ de serie de Fourier hiperbólica ]
[Ax][ x € C ]
x^{4} = ...
... (1/5)·pi^{4}+sum[k = 1]-[oo][ ( ( 8pi^{2}·(1/k)^{2}+(-48)·(1/k)^{4} )·cosh(k·pi·i) )·cosh(kx) ]
Teorema:
sum[k = 1]-[oo][ (1/k)^{4} ] = (1/90)·pi^{4}
sum[k = 1]-[oo][ (-1)^{k}·(1/k)^{4} ] = (-1)·(7/720)·pi^{4}
Series de Fourier-Laplacianas:
Definición:
f(x+vt) = ...
... (1/pi)·int[x = 0]-[pi][f(x)]d[x]+sum[k = 1]-[oo][ ...
... (1/pi)·int[(1/c)·(x = pi)]-[|w_{k}|(x+vt)][g(x)]d[x]·...
... (1/pi)·int[x = 0]-[pi][f(x)]d[x]·...
... (1/k)^{2}·(1/ln(2))·sin(k·(x+vt)) ]
( f(pi) & f(-pi) ) <==> |w_{k}| = pi
f(x+vt) = ...
... (1/(pi·i))·int[x = 0]-[pi·i][f(x)]d[x]+sum[k = 1]-[oo][ ...
... (1/(pi·i))·int[(1/c)·(x = pi)]-[(-1)·|w_{k}|(x+vt)][g(x)]d[x]·...
... (1/(pi·i))·int[x = 0]-[pi·i][f(x)]d[x]·...
... (1/k)^{2}·(1/ln(2))·sinh(k·(x+vt)) ]
( f(pi·i) & f((-pi)·i) ) <==> |w_{k}| = (-pi)
Definición:
f(x+vt) = ...
... int[x = 0]-[pi][f(x)]d[x]+sum[k = 1]-[oo][ ...
... (1/pi)·( ...
... int[(1/a)·(x = pi)]-[|a_{k}|(x+vt)][g(x)]d[x]+int[(1/b)·(x = pi)]-[|b_{k}|(x+vt)][h(x)]d[x] ...
... )·int[x = 0]-[pi][f(x)]d[x]·...
... (1/k)^{2}·(1/ln(2))·sin(k·(x+vt)) ]
( f(pi) & f(-pi) ) <==> |w_{k}| = pi
f(x+vt) = ...
... int[x = 0]-[pi·i][f(x)]d[x]+sum[k = 1]-[oo][ ...
... (1/(pi·i))·( ...
... int[(1/a)·(x = pi)]-[(-1)·|a_{k}|(x+vt)][g(x)]d[x]+int[(1/b)·(x = pi)]-[(-1)·|b_{k}|(x+vt)][h(x)]d[x] ...
... )·int[x = 0]-[pi·i][f(x)]d[x]·...
... (1/k)^{2}·(1/ln(2))·sinh(k·(x+vt)) ]
( f(pi·i) & f((-pi)·i) ) <==> |w_{k}| = (-pi)
Teorema:
[Ax][ x € R ]
f(ax+(2pi)·a) = f(ax) & f(ax+(-1)·(2pi)·a) = f(ax)
( x = 0 || vt = 0 )
(a·(x+vt))^{2n} = ...
... ( 1/(2n+1) )·(a·pi)^{2n}+...
... sum[k = 1]-[oo][ ...
... (1/pi)·( ((2n+1)·|w_{k}|(x+vt)+(-pi))/(2n+1) )·(a·pi)^{2n}·(1/k)^{2}·(1/ln(2))·sin(k·(x+vt)) ]
Teorema:
[Ax][ x € C ]
f(ax+(2pi·i)·a) = f(ax) & f(ax+(-1)·(2pi·i)·a) = f(ax)
( x = 0·i || vt = 0·i )
(a·(x+vt))^{2n} = ...
... ( 1/(2n+1) )·(a·pi·i)^{2n}+...
... (-1)·sum[k = 1]-[oo][ ...
... (1/(pi·i))·( ((2n+1)·|w_{k}|(x+vt)+pi)/(2n+1) )·(a·pi·i)^{2n}·(1/k)^{2}·(1/ln(2))·sinh(k·(x+vt)) ]
sinh(kxi) = i·sin(kx)
Teorema:
[Ax][ x € R ]
( x = 0 || vt = 0 )
e^{(2n+1)·(x+vt)·i} = ...
... (-1)·(1/(2n+1))·(2/(pi·i))+...
... sum[k = 1]-[oo][ ...
... (1/pi)·( (2n+1)·(i/2)·( |w_{k}|(x+vt) )^{2}+(-pi) )·
... (-1)·(1/(2n+1))·(2/(pi·i))·(1/k)^{2}·(1/ln(2))·sin(k·(x+vt)) ]
Teorema:
[Ax][ x € C ]
( x = 0·i || vt = 0·i )
e^{(2n+1)·(x+vt)} = ...
... (-1)·(1/(2n+1))·(2/(pi·i))+...
... sum[k = 1]-[oo][ ...
... (1/(pi·i))·( (2n+1)·(i/2)·( |w_{k}|(x+vt) )^{2}+(-pi) )·
... (-1)·(1/(2n+1))·(2/(pi·i))·(1/k)^{2}·(1/ln(2))·sinh(k·(x+vt)) ]
Teorema:
|w_{k}|(x+vt) = ...
... ( ( (-1)·0·e^{(2n+1)·(x+vt)·i}·pi^{2}+(-1)·pi·(2/i)·(1/(2n+1)) )·k^{2}·ln(2)·(1/sin(k·(x+vt)) )+...
... pi·(2/i)·(1/(2n+1)) )^{(1/2)}
|w_{k}|(x+vt) = ...
... ( ( (-1)·0·e^{(2n+1)·(x+vt)}·pi^{2}+(-1)·pi·(2/i)·(1/(2n+1)) )·k^{2}·ln(2)·(1/sin((k/i)·(x+vt)) )+...
... pi·(2/i)·(1/(2n+1)) )^{(1/2)}
Teorema:
[Ax][ x € R ]
( x = 0 || vt = 0 )
sin((2n+1)·(x+vt)} = ...
... (1/(2n+1))·2+...
... sum[k = 1]-[oo][ ...
... ( (1/pi)·(2n+(-1))·(2n+1)·(1/2)·( ( |a_{k}|(x,vt) )+(-1)·pi )+...
... (1/pi)·( (2n)·( |b_{k}|(x+vt)+(-pi) )+(-pi) ) )·
... (1/(2n+1))·2·(1/k)^{2}·(1/ln(2))·sin(k·(x+vt)) ]
Teorema:
[Ax][ x € C ]
( x = 0·i || vt = 0·i )
sinh((2n+1)·(x+vt)} = ...
... (-1)·(1/(2n+1))·2+...
... sum[k = 1]-[oo][ ...
... (-1)·( (1/(pi·i))·(2n+(-1))·(2n+1)·(1/2)·( ( |a_{k}|(x,vt) )+pi )+...
... (1/(pi·i))·( (2n)·( |b_{k}|(x+vt)+pi )+pi ) )·
... (-1)·(1/(2n+1))·2·(1/k)^{2}·(1/ln(2))·sinh(k·(x+vt)) ]
Teorema:
d_{vt}[ f(x+(1 || kvt)) ] = d_{x+(1 || kvt)}[ f(x+(1 || kvt)) ] [o(1 || vt)o] kvt
Demostración:
d_{vt}[ f(x+(1 || kvt)) ] = d_{x+(1 || kvt)}[ f(x+(1 || kvt)) ]·d_{vt}[ x+(1 || kvt) ] = ...
d_{x+(1 || kvt)}[ f(x+(1 || kvt)) ]·( d_{vt}[x]+d_{vt}[ (1 || kvt) ] ) = ...
d_{x+(1 || kvt)}[ f(x+(1 || kvt)) ]·( 0+(0 || k) ) = ...
d_{x+(1 || kvt)}[ f(x+(1 || kvt)) ]·k = d_{x+(1 || kvt)}[ f(x+(1 || kvt)) ] [o(1 || vt)o] kvt
Laplaciano-Físico con series de Fourier-Laplacianas:
Ley:
d_{xx}^{2}[u(x,t)] = (1/v)^{2}·d_{tt}^{2}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = 0·r ]
k = [ (1/metro) ]
u(x,t) = (1/pi)·int[x = 0]-[pi][ f(ax) ]d[x]+sum[k = 1]-[oo][ ...
... ( ...
... (1/pi)·int[(1/c)·(x = pi)]-[|w_{k}|(x+(-1)·(1/n)+((1/n) || vt))][ g(x) ]d[x]·...
... (1/pi)·int[x = 0][pi][ f(ax) ]d[x] ...
... (1/k)^{2}·(1/ln(2))·sin(kx+(-1)+(1 || kvt))
... ) ...
... ]
Deducción:
d_{vt}[ sin(kx+(-1)+(1 || kvt)) ] = cos(kx+(-1)+(1 || kvt)) [o(1 || vt)o] kvt
d_{vt}[ |w_{k}|(x+(-1)·(1/k)+((1/k) || vt)) ] = ...
... d_{x+(-1)·(1/k)+((1/k) || vt)}[ |w_{k}|(x+(-1)·(1/k)+((1/k) || vt)) ] [o(1 || vt)o] vt
Laplaciano-Físico con series de Fourier:
Ley:
d_{xx}^{2}[u(x,t)] = (1/v)^{2}·d_{tt}^{2}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = (1/(2pi))·int[x = (-pi)]-[pi][ f(ax) ]d[x]+sum[k = 1]-[oo][ ...
... ( ...
... (1/pi)·int[x = (-pi)][pi][ f(ax)·cos(kx) ]d[x]·cos(kx)+...
... (1/pi)·int[x = (-pi)][pi][ f(ax)·sin(kx) ]d[x]·sin(kx) ...
... )·cos(kvt) ...
... ]
Series de Garriga:
Definición:
f(x) = sum[k = 1]-[oo][ a_{k}·h_{k}(x) ]
Teorema:
0·f(x)·( 1/h_{k}(x) ) = a_{k}
Teorema:
f(x) = sum[k = 1]-[oo][ (1/w)·int[x = 0][w][ 0·f(x)·( 1/h_{k}(x) ) ]d[x]·h_{k}(x) ]
Teorema:
f(ax) = sum[k = 1]-[oo][ 0·f(ax) ]
Teorema:
(ax)^{p+n} = sum[k = 1]-[oo][ 0·( a^{p+n}·( w^{p}/(p+1) ) )·x^{n} ]
w = (p+1)^{(1/p)}·x
e^{p·ax} = sum[k = 1]-[oo][ 0·(1/w)·er-h[0](p·aw)·x ]
w = (1/(pa))·Anti-pow[(-1)]-er-h[0]( (1/(pa))·e^{p·ax}·(1/x) )
Teorema:
e^{p·(ax)} = sum[k = 1]-[oo][ 0·(1/w)·( e^{((pa)+(-k))·w}/((pa)+(-k)) )·e^{kx} ]
w = ( 1/(pa+(-k)) )·Anti-pow[(-1)]-e( e^{((pa)+(-k))·x} )
(ax)^{p} = sum[k = 1]-[oo][ 0·( ( (aw)^{p}/(p+1) ) [o(w)o] (-1)·(1/k)·e^{(-k)·w} )·e^{kx} ]
w = (-1)·(1/k)·Anti-pow[p]-[o(x)o]-e( (1/a)^{p}·(-k)^{p+1}·(p+1)·(ax)^{p}·e^{(-k)·x} )
Serie de Garriga Lineal:
Definición:
f(x) = sum[k = 1]-[oo][ a_{k}·kx ]
Teorema:
0·f(x)·(1/(kx)) = a_{k}
Teorema:
f(x) = sum[k = 1]-[oo][ (1/w)·int[x = 0][w][ 0·f(x)·(1/(kx)) ]d[x]·kx ]
Garriguense-Físico:
Ley:
d_{x}[u(x,t)] [o] u(x,t) = (1/v)·d_{t}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = sum[k = 1]-[oo][ ...
... (1/w)·int[x = 0][w][ 0·f(ax)·(1/(kx)) ]d[x]·kx·...
... ( 1 || (1/w)·int[x = 0][w][ 0·f(ax)·(1/(kx)) ]d[x]·(-1)·kvt )^{(-1)} ]
Deducción:
d_{vt}[ ( 1 || a_{k}·(-1)·kvt )^{(-1)} ] = ( 1 || a_{k}·(-1)·kvt )^{(-2)} [o(1 || vt)o] a_{k}·kvt
Se define r = a_{k}·kv
Si a = 1 ==> d_{vt}[u(x,0)] = r·0
Si a = vt ==> d_{x}[u(x,t)]·u(x,t) = (1/v)·d_{t}[u(x,t)]
Ley:
d_{x}[u(x,t)] [o] ( u(x,t) )^{[o] n} = (1/v)·d_{t}[u(x,t)]
u(x,0) = ( f(ax) )^{(1/n)} & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = sum[k = 1]-[oo][ ...
... ( (1/w)·int[x = 0][w][ 0·f(ax)·(1/(nkx)) ]d[x]·nkx )^{(1/n)}·...
... ( 1 || (1/w)·int[x = 0][w][ 0·f(ax)·(1/(nkx)) ]d[x]·(-n)·kvt )^{(-1)·(1/n)} ...
... ]
Deducción:
d_{vt}[ ( 1 || a_{k}·(-n)·kvt )^{(-1)·(1/n)} ] = ...
... ( 1 || a_{k}·(-n)·kvt )^{(-1)·( (1/n)+1 )} [o(1 || vt)o] (a_{k}·kvt)
Se define r = a_{k}·kv
Serie de Garriga de la divergencia:
Definición:
f(x) = sum[k = 1]-[oo][ a_{k}·e^{kx} ]
Teorema:
0·f(x)·e^{(-1)·kx} = a_{k}
Teorema:
f(x) = sum[k = 1]-[oo][ (1/w)·int[x = 0][w][ 0·f(x)·e^{(-1)·kx} ]d[x]·e^{kx} ]
Divergencia-Física:
Ley:
d_{x}[u(x,t)] = (1/v)·d_{t}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = sum[k = 1]-[oo][ ...
... (1/w)·int[x = 0][w][ 0·f(ax)·e^{(-1)·kx} ]d[x]·e^{kx}·(1/e)·e^{(1 || kvt)} ...
... ]
Divergencia-Lineal-Física:
Ley:
d_{x}[u(x,t)]+b·u(x,t) = (1/v)·d_{t}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = sum[k = 1]-[oo][ ...
... (1/w)·int[x = 0][w][ 0·f(ax)·e^{(-1)·kx} ]d[x]·e^{kx}·(1/e)·e^{(1 || (b+k)·vt)} ...
... ]
Serie de Garriga del Calor:
Definición:
f(x) = sum[k = 1]-[oo][ a_{k}·e^{(-1)·kx} ]
Teorema:
0·f(x)·e^{kx} = a_{k}
Teorema:
f(x) = sum[k = 1]-[oo][ (1/w)·int[x = 0][w][ 0·f(x)·e^{kx} ]d[x]·e^{(-1)·kx} ]
Calor-Matemático:
Ley:
d_{x}[u(x,t)] = (1/a)·d_{tt}^{2}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = sum[k = 1]-[oo][ ...
... (1/w)·int[x = 0][w][ 0·f(ax)·e^{kx} ]d[x]·e^{(-1)·kx}·cos( (ka)^{(1/2)}·t ) ...
... ]
Calor-Lineal-Matemático:
Ley:
d_{x}[u(x,t)]+b·u(x,t) = (1/a)·d_{tt}^{2}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = sum[k = 1]-[oo][ ...
... (1/w)·int[x = 0][w][ 0·f(ax)·e^{kx} ]d[x]·e^{(-1)·kx}·cos( ( ((-b)+k)·a )^{(1/2)}·t ) ...
... ]
Ecuación de Srödinguer:
Ley:
d_{xx}^{2}[u(x,t)]+(1/h)^{2}·( m·E((2n+1),(r/a),s) )·u(x,t) = (m/h)·d_{t}[u(x,t)]
u(x,0) = f(ax) & [Er][ d_{vt}[u(x,0)] = r·0 ]
k = [ (1/metro) ]
u(x,t) = (1/(2pi))·int[x = (-pi)][pi][f(ax)]d[x]+sum[k = 1]-[oo][ ...
... ( ...
... (1/pi)·int[x = (-pi)][pi][ f(ax)·cos(kx) ]d[x]·cos(kx)+...
... (1/pi)·int[x = (-pi)][pi][ f(ax)·sin(kx) ]d[x]·sin(kx) ...
... )·(1/e)·e^{( 1 || ( (1/h)^{2}·( m·E((2n+1),(r/a),s) )+(-1)·k^{2} )·(h/m)·t )} ...
... ]
E((2n+1),(r/a),s) = niveles de energía de los orbitales.
k = spin.
Ley:
Si está libre de pecado,
y es fiel,
no le tiréis la primera piedra.
Si no está libre de pecado,
y es infiel,
tirad-le la primera piedra.
Ley:
No existe delito de odio.
Si comete adulterio un homosexual pecador,
se le puede apedrear.
No existe delito de amor.
Si no comete adulterio un homosexual pecador,
no se le puede apedrear.
Ley:
Odio del mundo de un supositorio,
de adulterio de duales.
Odio del mundo de pegar-te en el culo,
de apedrear de duales.
Ley:
Odio del mundo de chocho apestoso,
de adulterio de duales.
Odio del mundo de pegar-te delincuentes,
de apedrear de duales.
Ley:
Odio del mundo se semen en la cara,
de adulterio de duales.
Odio del mundo de tortas en la cara,
de apedrear de duales.
Ley:
Odio del mundo mirar pollas,
de adulterio de imagen de duales.
Odio del mundo decir-te homosexual,
de adulterio de sonido de duales.
Ley:
Odio del mundo cerrar-te en un hospital psiquiátrico,
de robar la libertad en la propiedad de hacer dinero.
Odio del mundo visitar-te en casa el psiquiatra,
de robar la intimidad en la propiedad de hacer dinero.
Ley:
Odio del mundo no me gusta tu música.
Odio del mundo no me gusta como danzas.
Ley:
Odio del mundo no me gusta tus videos.
Odio del mundo no me gusta como juegas a videojuegos.
Teorema:
[As][ s > 0 ==> lim[n = oo][ | a+(-a) |+(-s) < | a+(-1)·a_{n} | < | a_{n}+(-1)·a_{n} |+s ] ]
Teorema:
lim[n = oo][ n ] = oo
Demostración:
Sea s > 0 ==>
lim[n = oo][ 1+(-s) < | oo+(-n) | < 1+s ]
Ley: [ de Laplace-D'Alembert ]
d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (1/v)^{2}·d_{tt}^{2}[u(x,y,t)]
u(x,y,0) = (ax)^{p}+(ay)^{q} & [Er][ d_{vt}[u(x,y,0)] = r·0 ]
a = [ (1/metro) ]
u(x,y,t) = (1/2)·( ( a·(x+vt) )^{p}+( a·(y+vt) )^{q} )+( a·(x+(-v)·t) )^{p}+( a·(y+(-v)·t) )^{q} ) )
Ley: [ de Laplace-D'Alembert ]
d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (1/v)^{2}·d_{tt}^{2}[u(x,y,t)]
u(x,y,0) = bxy & [Er][ d_{vt}[u(x,y,0)] = r·0 ]
b = [ (1/metro)^{2} ]
u(x,y,t) = (1/2)·( ...
... b·(x+vt)^{1+(0 || 1 || 2)}·(y+vt)^{1+(0 || 1 || 2)} )+...
... b·(x+(-v)·t)^{1+(0 || 1 || 2)}·(y+(-v)·t)^{1+(0 || 1 || 2)} )
Definición:
d_{x...x}^{n}[ x^{p+(0 || ...|| n)} ] = p^{n}·x^{p+(-n)+(0 || ...|| n)} = p^{n}·x^{p}
Teorema:
d_{x}[ f(x & oo·x) ] = d_{x & oo·x}[f(x & oo·x)] [o(1 || x)o] oo·x
Demostración:
d_{x}[ f(x & oo·x) ] = d_{x & oo·x}[f(x & oo·x)]·d_{x}[ (x & oo·x) ] = ...
... d_{x & oo·x}[f(x & oo·x)]·(oo || 1) = d_{x & oo·x}[f(x & oo·x)]·oo = ...
... d_{x & oo·x}[f(x & oo·x)] [o(1 || x)o] oo·x
Teorema:
d_{x}[ f(x & 0·x) ] = d_{x & 0·x}[f(x & 0·x)] [o(1 || x)o] x
Demostración:
d_{x}[ f(x & 0·x) ] = d_{x & 0·x}[f(x & 0·x)]·d_{x}[ (x & 0·x) ] = ...
... d_{x & 0·x}[f(x & 0·x)]·(0 || 1) = d_{x & 0·x}[f(x & 0·x)] = ...
... d_{x & 0·x}[f(x & 0·x)] [o(1 || x)o] x
Examen:
Teorema:
d_{x}[ f(x & nx) ] = d_{x & nx}[f(x & nx)] [o(1 || x)o] nx
d_{x}[ f(x & (1/n)·x) ] = d_{x & (1/n)·x}[f(x & (1/n)·x)] [o(1 || x)o] x
Ley: [ de Plank-D'Alembert ]
d_{xx}^{2}[u(x,t)] = (m/h)·d_{t}[u(x,t)]
u(x,0) = (ax)^{p} & [Er][ d_{t}[u(x,0)] = r·0 ]
a = [ (1/metro) ]
u(x,t) = (ax+pa^{2}·(h/m)·( (t || 1)+(-1) ) )^{p+(0 || 1 || 2)}
Ley: [ de Plank-D'Alembert ]
d_{xx}^{2}[u(x,t)] = (m/h)·d_{t}[u(x,t)]
u(x,0) = e^{p·ax} & [Er][ d_{t}[u(x,0)] = r·0 ]
a = [ (1/metro) ]
u(x,t) = e^{p·ax+(pa)^{2}·(h/m)·( (t || 1)+(-1))}
Ley: [ de Plank-D'Alembert ]
d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (m/h)·d_{t}[u(x,y,t)]
u(x,y,0) = bxy & [Er][ d_{t}[u(x,y,0)] = r·0 ]
a = [ (1/metro) ]
u(x,y,t) = ...
... ( b^{(1/2)}·x+b·(h/m)·( (t || 1)+(-1) ) )^{1+(0 || 1 || 2)}·...
... ( b^{(1/2)}·y+b·(h/m)·( (t || 1)+(-1) ) )^{1+(0 || 1 || 2)}
Ley: [ de Srôdinguer-D'Alembert ]
d_{xx}^{2}[u(x,t)]+(1/h)^{2}·( m·E((2n+1),(r/a),s) )·u(x,t) = (m/h)·d_{t}[u(x,t)]
u(x,0) = (ax)^{p} & [Er][ d_{t}[u(x,0)] = r·0 ]
a = [ (1/metro) ]
u(x,t) = ( (ax+((1/p)·(1/h)^{2}·m·E((2n+1),(r/a),s)+pa^{2})·(h/m)·( (t || 1)+(-1) ) )^{p+(0 || 1 || 2)}
Teorema:
Profesor Jûanat-Hád.
Alumno Peter-Hád.
Demostración
Profesor Jean D'Alenbert
Alumno Pierre-Simón de Laplace.
Teorema:
No sigue la gente a Jûanat-Hád ni a Peter-Hád,
porque sinó no habría odio del mundo en televisión.
Demostración:
Siguiría la gente a Jûanat-Hád o a Peter-Hád,
aunque no-obstante habría odio del mundo en televisión.
Ley:
Odio del mundo de destrucción del alma,
de matarás.
Odio del mundo de violación psíquica,
de adulterio.
Anexo:
Vigilad de poner-le motivo al odio del mundo.
Ley:
Odio del mundo de medicar-te con clozapina,
de honrarás al padre y a la madre en el Caos.
Odio del mundo de hacer-te análisis de sangre,
de des-honrarás al padre y a la madre en la Luz.
Anexo:
Es imposible que yo sea homosexual,
porque estaría muerto de la clozapina.
Ley:
Odio del mundo de análisis de orina,
de honrarás al padre y a la madre en el Caos.
Odio del mundo de análisis de sangre,
de des-honrarás al padre y a la madre en la Luz.
Ley:
Odio del mundo de percepción en la Fuerza de terror ansiedad,
de matarás.
Odio del mundo de percepción en la Fuerza de violación,
de adulterio.
