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A systematic derivation is presented of Lekhnitsky's approach (J. Appl. Math. Mech., USSR Acad. Sci. 4, no. 3:43, 1940) to problems with torsionless axisymmetry in a medium possessing transverse isotropy. The derivation is preceded by a generalization of a theorem of Almansi (Ann. di Mat. ser. 3, vol. 2, 1899) concerning the representation of the general solution of Delta 2n F=0 in terms of harmonic functions.
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Eubanks et al. (1954) studied this question.
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