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Mathematics
Mathematics
Problem
Let
J
n
=
∫
0
π
/
2
cos
n
x
d
x
J_n = \displaystyle \int_{0}^{\pi/2} \cos^{n}x\,dx
J
n
=
∫
0
π
/2
cos
n
x
d
x
for integers
n
≥
2
n\ge 2
n
≥
2
. Derive a recurrence formula that relates
J
n
J_n
J
n
to
J
n
−
2
J_{n-2}
J
n
−
2
.
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