integral de serie geométrica

∫ [ e^{x}·( (x^{(n+1)}+(-1))/(x+(-1)) ) ] d[x] = e^{x}+∑ ( x^{(k+1)}·er_{m;k+1}(x) )


∫ [ e^{x}·( (x^{(n+1)}+(-1))/(x+(-1)) ) ] d[x]= ∫ [ e^{x}+∑ ( e^{x}·x^{k} ) ] d[x]


∫ [ e^{(-x)}·( (x^{(n+1)}+(-1))/(x+(-1)) ) ] d[x] = (-1)·( e^{(-x)}+∑ ( (-x)^{(k+1)}·er_{m;k+1}(-x) ) )

índex de física

índex de etiquetes de física

álgebra: índex-algebràic de un grup normal

A={1,3,5}
B={2,4,6}
C={3,5,7}


A+{1}={0}+B
A+{0}={(-1)}+B


A+{2}={0}+C
A+{0}={(-2)}+C


B+{1}={0}+C
B+{0}={(-1)}+C


E={1,3,5}
F={5,15,25}
G={2,6,10}


E·{5}={1}·F
E·{1}={(1/5)}·F


E·{2}={1}·G
E·{1}={(1/2)}·G


F·{(2/5)}={1}·G
F·{1}={(5/2)}·G

álgebra: sistema cuadrat

x^{2}+y^{2} =  p
x+y = q


(x+y)^{2}+(-2)xy = p


q^{2}+(-p) = 2xy


x^{2}+(q+(-x))^{2} =  p
(q+(-y))^{2}+y^{2} =  p


2x^{2}+(-2)qx+q^{2} =  p
2y^{2}+(-2)qy+q^{2} =  p


x^{2}+(-q)x+( (q^{2}+(-p))/2 ) =  0
y^{2}+(-q)y+( (q^{2}+(-p))/2 ) =  0


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

álgebra: exponent directe cuadrat

a^{2}+b^{2} = (1/2)( (a+b)^{2}+(a+(-b))^{2} )


1+4 = 5 = (1/2)( ( 1+2 )^{2}+( 2+(-1) )^{2} )
4+4 = 8 = (1/2)( ( 2+2 )^{2}+( 2+(-2) )^{2} )


1+9 = 10 = (1/2)( ( 1+3 )^{2}+( 3+(-1) )^{2} )
4+9 = 13 = (1/2)( ( 2+3 )^{2}+( 3+(-2) )^{2} )
9+9 = 18 = (1/2)( ( 3+3 )^{2}+( 3+(-3) )^{2} )


1+16 = 17 = (1/2)( ( 1+4 )^{2}+( 4+(-1) )^{2} )
4+16 = 20 = (1/2)( ( 2+4 )^{2}+( 4+(-2) )^{2} )
9+16 = 25 = (1/2)( ( 3+4 )^{2}+( 4+(-3) )^{2} )
16+16 = 32 = (1/2)( ( 4+4 )^{2}+( 4+(-4) )^{2} )

índex de matemàtiques

index de etiquetes matemàtiques

índex de etiquetes

index de etiquetes.