This works in the developement version 6.4.beta1. This should work the same in 6.3.
sage: sum(-1**(i+1)/(2*i-1)**3*(sin(pi*(2*i-1)/2*(r1+r2))*sin(pi*(2*i-1)/2*(r1-r2))),i,1,oo)
-1/4*(-I*imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r1))) - I*imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r1))) - real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r1))) - real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r1))))*cos(pi*r1) - 1/4*(I*imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r2))) + I*imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r2))) + real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r2))) + real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r2))))*cos(pi*r2) - 1/4*(imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r1))) - imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r1))) - I*real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r1))) + I*real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r1))))*sin(pi*r1) + 1/4*(imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r2))) - imag_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r2))) - I*real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(2*I*pi*r2))) + I*real_part(hypergeometric((1/2, 1/2, 1/2, 1), (3/2, 3/2, 3/2), e^(-2*I*pi*r2))))*sin(pi*r2)
