serie

(1/pi)·int[ x^{2}·cos(kx) ] d[x] = ...

(1/pi)·(1/k)·int[ x^{2}·cos(kx)·k ] d[x] = ...

(1/pi)·(1/k)·( x^{2}sin(kx)+(-1)·int[ 2x·sin(kx) ] d[x] ) =

pi^{2} = (pi^{2}/3)+4·sum[ (1/k^{2}) ]

(1/pi)·int[ (-x)·sin(kx) ] d[x] = ...

(1/pi)·(1/k)·x·cos(kx)+(-1)·int[ cos(kx) ] d[x]

pi = (pi/2)+sum[ (1/k) ]

sum[ (1/k) ] = (1/2)·pi

0 < x < pi

(1/pi)·( int[ (-x)^{3}·sin(kx) ] d[x]+(-2)·(1/k^{2})·int[ (-x)·sin(kx) ] d[x] ) = ...

(1/k^{2})·int[ 3·(-x)^{2}·cos(kx)·k ] d[x] = ...

... (1/k^{2})·( 3·(-x)^{2}·(-1)·sin(kx)+(-1)·int[ 6x·sin(kx) ] d[x] )

pi^{3} = (pi^{3}/4)+(pi^{3}/2)+5·sum[ (1/k^{3}) ]

sum[ (1/k^{3}) ] = (pi^{3}/20)