[VA] SRC#001 - Spiky Integral

[Pjwum]

With HP Prime

Code:


EXPORT SPIKES()
BEGIN
LOCAL N;
FOR N FROM 1 TO 20 DO
PRINT(int(product(COS(M*X),M,1,N,1),X,0,2*π));
END;
END;

we can go beyond 10

0
0
1/2 pi
1/4 pi
0
0
1/8 pi
7/64 pi
0
0
35/512 pi
31/512 pi
0
0
361/8192 pi
657/16384 pi
0
0
2055/65536 pi
1909/65536 pi

suggesting that I(N) will be non-zero if and only if
N = 4k+3 and N = 4k+4, for k = 0, 1, 2..