Kosinusreihe
n
P
2k
2n
x
(−1)k (2k
)! ,
x
(n ∈ N0 )
an := (−1)n (2n)!
k =0
x 2n Abbruch der Summation, falls (−1)n (2n)!
≤ ε|sn |
x 2n d.h. Fortsetzung der Summation, solange (−1)n (2n)!
> ε|sn |
sn :=
Rekursion:
a0 = 1,
s0 = 1,
Pseudocode
2
x
an = −an−1 2n(2n−1)
(n ∈ N)
sn = sn−1 + an (n ∈ N)
[Formulierung in Worten]
s0 = 1; a0 = 1; n = 1;
while (|an−1 | > ε|sn−1 |) {
x2
an = −an−1 · 2n(2n−1)
;
sn = sn−1 + an ;
n →n+1
}
Kosinusreihe - Fortsetzung
Programmfragment
s = 1; a = 1; n = 1;
// s: s0 , a: a0
while (abs(a)>eps*abs(s)) {
// s: sn−1 , a: an−1
a = -a*x*x/(2*n*(2*n-1));
x2
= an
// a: −an−1 · 2n(2n−1)
s = s+a;
// s: sn−1 + an = sn
n = n+1;
// s: sn−1 , a: an−1
}

Pseudocode Interpreter