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THE LAPLACE TRANSFORM
Ill FOURIER TRANSFORMS
HANKEL AND MELLIN TRANSFORMS
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applied auxiliary equations Bessel Functions biharmonic equation boundary conditions boundary-value problems Cambridge Phil complex Fourier transform conduction of heat constant cosh cospx denotes dual equations dual integral equations dV/dx E. T. Whittaker Edinburgh Math elastic electrified disc evaluated EXAMPLES ON CHAPTER finite Hankel transform finite sine transform Fourier's integral formula G. N. Watson given gives Glasgow Math heat conduction Hence independent variables infinite initial condition integral transform integrand integrating with respect inversion formula Jacobi polynomials Journ Journal Mech kernel Laplace transform Legendre transforms limit line integral Mellin transform numerical obtained ordinary differential equation partial differential equation physical problems plane poles positive integer positive roots Proc px dx Quart result satisfies semi-infinite solid shear stress sine or cosine Sneddon solution of boundary-value solved summation tends to infinity tends to zero term tion transform defined transform to show wanted function write written xp dp zero temperature