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Displaying similar documents to “Integrals involving products of E -functions, Bessel-functions and generalized hypergeometric functions.”

Construction of the solutions of boundary value problems for the biharmonic operator in a rectangle

Nachman Aronszajn, R. D. Brown, R. S. Butcher (1973)

Annales de l'institut Fourier

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A technique is developed for constructing the solution of Δ 2 u = F in R = { ( x , y ) : | x | < a , | y | < b } , subject to boundary conditions u = φ , u n = ψ on R . The problem is reduced to that of finding the orthogonal projection P w of w in L 2 ( R ) onto the subspace H of square integrable functions harmonic in R . This problem is solved by decomposition H into the closed direct (not orthogonal) sum of two subspaces H ( 1 ) , H ( 2 ) for which complete orthogonal bases are known. P is expressed in terms of the projections P ( 1 ) , P ( 2 ) of L 2 ( R ) onto H ( 1 ) , H ( 2 ) respectively. The resulting...