Chaue Centrale  2/3 TP Python

f:x > 07→ sin x
x−1·
f f R∗
+
A=Z+∞
0
f(x)dx ∀a > 0, F (a) = Za
0
f(x)dx.
x > 0t−1>t/2t>x
a|F(a)−A|610−5
F(a)
]0, a] ]0,+∞[
(an)n∈N∗
Z+∞
0
f(x)dx =
+∞
X
n=1
an.
A N  A−
N
P
k=1
ak 610−5
a1=A an= 0 n>2

P0= 1 P1= 2X
∀n∈N, Pn+2 = 2XPn+1 −Pn
Pnn68
Pn
∀P, Q ∈R8[X], <P |Q>=2
πZ1
−1
P(t)Q(t)p1−t2dt
<Pi|Pj>06i, j 68
B= (P0, ..., P8)
Φ : P7−→ −3XP 0+ (1 −X2)P00
R8[X]B
Φ
Φ
ϕ(t)
x=t
1 + t3
y=t2
1 + t3
F(x, y)=0
ϕ(t1)ϕ(t2)ϕ(t3)t1t2t3=−1
(m, n)∈N2um,n =Z1
0
xm(1 −x)ndx
um,0n > 0um,n
um,n

(m, n)
Z1
0
x6−4x5+ 5x4+ 4
4 + x4(1 −x)4=
+∞
X
k=0 −1
4kZ1
0
(x6−4x5+ 5x4+ 4)x4k(1 −x)4kdx
f
X3+Y3=XY