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let-r-0-1-and-x-R-and-x-r-arctan-rsinx-1-r-cosx-1-prove-that-x-x-r-n-1-r-n-cos-nx-2-prove-that-x-r-n-1-r-n-sin-nx-n-




Question Number 35609 by abdo mathsup 649 cc last updated on 21/May/18
let r ∈[0,1[ and x∈ R  and   ϕ(x,r) = arctan( ((rsinx)/(1−r cosx)))  1) prove that  (∂ϕ/∂x)(x,r)  =Σ_(n=1) ^∞  r^n  cos(nx)  2)prove that ϕ(x,r) = Σ_(n=1) ^∞  r^n   ((sin(nx))/n)
letr[0,1[andxRandφ(x,r)=arctan(rsinx1rcosx)1)provethatφx(x,r)=n=1rncos(nx)2)provethatφ(x,r)=n=1rnsin(nx)n

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