Thursday, 17 May 2018

integration - A sine integral

The integral
π/20sin(nθ)sin(θ) dθ
is claimed to not have a closed form expression. In this view find the series solution of the integral as a series involving of n.



Editorial note:
As described in the problem several series may be obtained, of which, all seem to hold validity. As a particular case, from notes that were made a long while ago, the formula
π/20sin(nθ)sin(θ) dθ=r=1(1)r1 ln(2r+12r1) sin(rnπ)
is stated, but left unproved. Can this formula be proven along with finding other series dependent upon n?

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