## The use of integral transforms |

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Applying arbitrary Bessel function boundary conditions boundary value problem coefficients constant converges convolution theorem cosh cosha coshx defined by equation definition denotes derive diffusion equation distribution dual integral equations easily shown equivalent example Find the solution finite Fourier Fourier cosine transform Fourier inversion theorem Fourier sine transform Fourier transform function f(x given half-plane half-space Hankel inversion theorem Hankel transform hence initial conditions initial value problem integral equation integral transforms interval inversion formula kernel Laplace transform Laplace's equation Legendre lemma linear Mellin transform method obtain the equation obtain the relation obtain the solution partial differential equation polynomial positive integer positive number Prob properties Prove real line required solution respect result right-hand side satisfies the conditions satisfying the boundary sequence Similarly simple sinh tends to zero theory transform of order write written