Periodic Delta Function and Poisson Integral for - Gauge-institute.org

Gauge Institute JournalH. Vic Dannon= + z(1 + z + z + ...)12= 1 +1z1 −z2=1 1+z21−z==1 12112+ re− reiϕiϕiϕ1+ re 1−reiϕ1−re1−re−iϕ−iϕ=21 r2 21− + 2irsinϕ1+ r −2rcosϕ21− rri2 2 21 sinϕ= +1+ r − 2r cosϕ1+ r −2rcosϕThe real part isThat is,1 2+1r cosϕ+ r cos 2 ϕ + ... =2 2 21 − r1+ r −2rcosϕ21 2 −2iϕ −iϕ iϕ 2 2iϕ1 1 − r2{ .. + r e + re + 1 + re + r e + ..}=2 2Thus, the Fourier Series may have Abel Sumξ=1∫ξ=−1f211 − r( ξ)lim r ↑12 12 2 cos π (dξ+ r − r x −ξ)21+ r −2rcosϕThe Poisson Integral associated with f ( x ) at r = 1− 0 + .6