ecuacions de camp

div[E(x,y,z)] = d_{xyz}^{3}[ anti-potencial[E(x,y,z)] ]

anti-div[E(x,y,z)] = d_{xyz}^{3}[ potencial[E(x,y,z)] ]

anti-potencial[ rot[E(x,y,z)] ] = 0

potencial[ anti-rot[E(x,y,z)] ] = 0

anti-potencial[ grad[ potencial[ rot[E(x,y,z)] ] ] ] = 0

potencial[ anti-grad[ anti-potencial[ anti-rot[E(x,y,z)] ] ] ] = 0

int[ anti-rot[E(x,y,z)] ]d[t] [o]-[o(t)o]-[o] int[ <x,y,z> ]d[t] = 0

int[ rot[E(x,y,z)] ]d[t] [o]-[o(t)o]-[o] int[ <yz,zx,xy> ]d[t] = 0

d_{t}[E(x,y,z)] = div-vectorial[ E(x,y,z) ]· ...

... < d_{t}[x],d_{t}[y],d_{t}[z] >

d_{tt}^{2}[E(x,y,z)] = anti-div-vectorial[ E(x,y,z) ]· ...

.. < d_{t}[y]d_{t}[z],d_{t}[z]d_{t}[x],d_{t}[x]d_{t}[y] >

d_{t...t}^{n}[E(x,y,z)] = n-div-vectorial[ E(x,y,z) ]·...

... < d_{t}[x]^{n},d_{t}[y]^{n},d_{t}[z]^{n} >

d_{tt...tt}^{2n}[E(x,y,z)] = anti-n-div-vectorial[ E(x,y,z) ]· ...

... < d_{t}[y]^{n}d_{t}[z]^{n},d_{t}[z]^{n}d_{t}[x]^{n},d_{t}[x]^{n}d_{t}[y]^{n} >

ecuació de ones:

m·d_{tt}^{2}[x_{k}] = q·( E(x_{k})+(-1)·E(d_{t}[x_{k}]·t) )

x_{k} = c_{k}t

d_{t...t}^{n}[ E(x,y,z)+(-1)·E(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...

... n-div-vectorial[ E(x,y,z)+(-1)·E(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ]· ...

... < (c_{x})^{n},(c_{y})^{n},(c_{z})^{n} >

d_{tt...tt}^{2n}[ E(x,y,z)+(-1)·E(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...

... anti-n-div-vectorial[ E(x,y,z)+(-1)·E(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ]· ...

... < (c_{y}c_{z})^{n},(c_{z}c_{x})^{n},(c_{x}c_{y})^{n} >

E(x) = (ct)^{n}

( n!/(n+(-k))! )·c^{n}·t^{n+(-k)}+(-1)·( n!/(n+(-k))! )·c^{n}·t^{n+(-k)} = ...

... ( ( n!/(n+(-k))! )·(ct)^{n+(-k)}+(-1)·( n!/(n+(-k))! )·(ct)^{n+(-k)} )·c^{k}