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Matrix elements of irreducible representations of the Lorentz group arecalculated on the basis of complex angular momentum. It is shown thatLaplace-Beltrami operators, defined in this basis, give rise to Fuchsiandifferential equations. An explicit form of the matrix elements of the Lorentzgroup has been found via the addition theorem for generalized sphericalfunctions. Different expressions of the matrix elements are given in terms ofhypergeometric functions both for finite-dimensional and unitaryrepresentations of the principal and supplementary series of the Lorentz group.Comment: 21 page

Relativistic spherical functions on the Lorentz group