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let-r-0-1-and-R-x-R-prove-that-1-1-2-n-1-r-n-cos-1-r-2-1-2r-cos-r-2-2-1-1-2pi-0-2pi-1-r-2-1-2rcos-t-x-r-2-dt-




Question Number 35605 by abdo mathsup 649 cc last updated on 21/May/18
let r∈[0,1[ and θ ∈ R,x∈ R prove that  1) 1+ 2 Σ_(n=1) ^(+∞)  r^n cosθ = ((1−r^2 )/(1−2r cosθ +r^2 ))  2)1 =(1/(2π)) ∫_0 ^(2π)       (((1−r^2 ))/(1−2rcos(t−x) +r^2 ))dt
letr[0,1[andθR,xRprovethat1)1+2n=1+rncosθ=1r212rcosθ+r22)1=12π02π(1r2)12rcos(tx)+r2dt

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