... 133−1−0 .5 00 .5 1−1−0 .5 00 .5 1−0.200.20.40.60.81xyu(r,θ )Figure 3.4.1:Thesolutionu(r, θ)tothe mixed boundary value problem posed in Example3.4.1 with α = π/4andb =0. 25. power ... and Ryzhik, op. cit., Formula 2. 252 , Point II.© 2008 by Taylor & Francis Group, LLC126 Mixed Boundary Value Problems 00 .5 11 .5 2−2−101201234 5 678910zru(r,z)Figure 3.3.8:Theelectrostatic ... Francis Group, LLC120 Mixed Boundary Value Problems where knis the nth positive root of J0(ka)=0. Equation 3.3.63 throughEquation 3.3. 65 satisfy Equation 3.3 .58 , Equation 3.3 .59 , Equation 3.3.60,andEquation...