How can I get exact analytical symbolic solution of a Cosine series from 1 up to nth harmonic?

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Mukul 2019-2-18

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https://ww2.mathworks.cn/matlabcentral/answers/445502-how-can-i-get-exact-analytical-symbolic-solution-of-a-cosine-series-from-1-up-to-nth-harmonic

Hi, I am trying to solve for

syms n  m d
m=2*n-1;
eqn1=symsum(1/m^2,n,1,Inf)
eqn = symsum(cos(m*d)/m^2,n,1,Inf)

I get the correct answer for sum of (1/m^2) equal to

eqn1 = pi^2/8

running that code. But when I try to get sum of cos(m*d)/m^2, it comes with the following expression even I assume and simplifiy it.

piecewise(in(d, 'real'), - exp(-d*1i)/2 - exp(d*1i)/2 + (exp(-d*1i)*hypergeom([-1/2, -1/2, 1], [1/2, 1/2], exp(d*2i)))/2 + (exp(d*1i)*hypergeom([-1/2, -1/2, 1], [1/2, 1/2], exp(-d*2i)))/2)

assume(d,'integer')
assume(d,'real')
assume(d<pi & d>-pi)
simplify(piecewise(in(d, 'real'), - exp(-d*1i)/2 - exp(d*1i)/2 + (exp(-d*1i)*hypergeom([-1/2, -1/2, 1], [1/2, 1/2], exp(d*2i)))/2 + (exp(d*1i)*hypergeom([-1/2, -1/2, 1], [1/2, 1/2], exp(-d*2i)))/2))

The simplified expression would be

pi^2/8(1-2*abs(d)/pi)

Can anyone suggest me whether is there any way to simplify the long piecewise equation into the above simple equation?

Any help is highly appreatiated.