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THE LAPLACE TRANSFORM
Ill FOURIER TRANSFORMS
HANKEL AND MELLIN TRANSFORMS
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applied appropriate arc tends asymptotic series auxiliary equations Bessel Functions biharmonic equation boundary conditions boundary-value problems Cambridge complex Fourier transform conduction of heat constant contour integral cosh curved surface denotes dV/dx EXAMPLES ON CHAPTER finite Hankel transform finite sine transform Fourier sine Fourier's integral formula G. N. Watson given gives H. S. Carslaw heat conduction Hence independent variables infinite initial condition initial temperature integral transform integrand integrating with respect inversion formula 1.10 kernel Laplace transform Legendre transform limit line integral Mellin transform obtained ordinary differential equation partial differential equation Phil poles positive roots Proc px dx range of integration real axis residues result satisfies semi-infinite solid shear stress sine or cosine sinh Sneddon solve stress function summation tends to infinity tends to zero term tion transform defined transform to show values wanted function write written xp dp zero temperature zp dp