i am trying to find coefficients a0 , an and bn but the output for bn seems wrong and will not simplify

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scott lamb
scott lamb 2020-11-30
评论： Matt J 2020-12-1
i am trying to find coefficients a0 , an and bn but the output for bn seems wrong and will not simplify
i have tried using pretty, symplify, ignoreanalyticconstraint,true and simplifyFraction, but none have worked
f(x) = -3, -pi < x < 0
f(x) = 3, 0 < x < pi
syms t n
T = 2*pi
w0 = 2*pi/T
n=1:5
a0 = (1/T)*int(3,t,-pi,0) + (1/T)*int(-3,t,0,pi)
an = (2/T)*int(-3*cos(n*w0*t),t,-pi,0) + (2/T)*int(3*cos(n*w0*t),t,0,pi)
bn = (2/T)*int(-3*sin(n*w0*t),t,-pi,0) + (2/T)*int(3*sin(n*w0*t),t,0,pi);
pretty(bn)

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回答（1 个）

Matt J
Matt J 2020-12-1
Well, here is what I get for bn,
>> bn
bn =
[ 17202483417667977/4503599627370496, 0, 5734161139222659/4503599627370496, 0, 17202483417667977/22517998136852480]
You haven't told us whether you get the same thing, or if so what you would expect instead, but these terms do look nice when multiplied by pi,
>> double(bn*pi)
ans =
12.0000 0 4.0000 0 2.4000
  2 个评论
Walter Roberson
Walter Roberson 2020-12-1
Ran in:
syms t n
Pi = sym(pi);
T = 2*Pi;
w0 = 2*Pi/T;
n=1:5
n = 1×5
1 2 3 4 5
a0 = (1/T)*int(3,t,-Pi,0) + (1/T)*int(-3,t,0,Pi)
a0 = 
0
an = (2/T)*int(-3*cos(n*w0*t),t,-Pi,0) + (2/T)*int(3*cos(n*w0*t),t,0,Pi)
an = 
bn = (2/T)*int(-3*sin(n*w0*t),t,-Pi,0) + (2/T)*int(3*sin(n*w0*t),t,0,Pi);
pretty(bn)
/ 12 4 12 \ | --, 0, --, 0, ---- | \ pi pi 5 pi /

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