ry''+py'+qy=0,
lim(x-xo)p/r=po,
lim(x-xo)^2q/r=qo,

y(x)=Sanx^n
     0
y'=SnanX^(n-1) ...

kanoume to x upswmeno
sthn idia dunamh
Sanx^n=S  an+k*x^(n+k)
no     no-k

-afhnoume kai orous ap'eksw
 gia na einai idia ta oria
 (ta psilotera)
bgazoume tis sxeseis kai
-poll/me kata melh opote
 vgainei tupos an=f(n) p.x.
-grafoume y(x)=..=(a0+a2x^2)+(a1x+...)=
 c1*Stupos1+c2*Stupos2
FROBENIUS:
lunw thn r(r-1)+po*r+qo=0
1.an r1-r2<>0,1,2 me (r1>r2)
 y1=x^r1SanX^n
 y2=x^r2SanX^n
2.An r1-r2=0,1,2 tote
 y1=x^r1SanX^n
 y2=cy1lnx+x^r2Sbnx^n , r2<=r1
h y2=x^r2SbnX^n

R=lim |an/a(n+1)|
  n->oo

R=lim1/sqrt(n)(|an|)

e^x=...+X^n/n!
cosx=..+(-1)^n*x^2n/(2n)!
sinx=..+(-1)^n*x^(2n+1)/(2n+1)!
ln(1+x)=..+(-1)^(n-1)*x^n/n suglinei gia |x|<1

