The Use of Integral Transforms |
Common terms and phrases
a₁ analytic b₁ Bessel function boundary conditions boundary value problem coefficients consider constant converges convolution theorem cosech cosh deduce defined by equation definition denotes derive diffusion equation dx² easily shown equivalent example Find the solution finite Fourier cosine transform Fourier sine transform Fourier transform function f(x half-plane Hankel transform hence initial conditions integral equation interval inversion formula inversion theorem kernel Laplace transform Laplace's equation lemma Mellin transform method obtain the relation obtain the solution operator partial differential equation polynomial positive integer positive number Prob Prove R₁ real line respect result right-hand side satisfies the conditions satisfying the boundary Similarly simple sinh Stieltjes transform tanh tends to zero variable write written πτ ди дх