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Note on the problem of heat conduction in a semiinﬁnite hollow
Formulas for complex interpolation
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airfoil angle applied approximation arbitrary assume axes axis bending Bessel functions biharmonic equation bipolar coordinates boundary conditions boundary value problem calculate coefficients column components computed consider constant convergence coordinates corresponding cosh curvature curve Danielewsky deﬁned deflection denote derivatives determined differential equations direction displacement distribution elastic elliptic equations of equilibrium expansion expression ﬁeld ﬁnd ﬁnite ﬁrst formula Fourier series given gives Hence impedance incompressible integral interpolation Laplace's equation linear load Math mathematical matrix membrane middle surface mode nonlinear normal obtained plane polynomial potential quantities R. V. Southwell ratio relaxation method residuals satisfy shearing stress sinh solution solved square strain subspace Substituting symmetry Table tensor theorem theory thin shells tion torsion transformation transmission vanish variable vector vector potential velocity velocity potential visco-elastic wave guide X X X zero