On a new approach to the theory of special functions

A new approach is presented to the construction of a theory of special functions, permitting one to consider from a single point of view the theories of the classical orthogonal polynomials (including, in particular, the polynomials of Legendre, Chebyshev, Laguerre and Hermite) and the theories of the spherical, cylindrical and hypergeometric functions. The comprehensiveness of the presentation is achieved by regarding all of the special functions as particular solutions of a differential equation of a certain form arising in many problems of mathematical physics and quantum mechanics. An integral representation is found for the solutions of this equation that yields in the sequel all of the basic properties of the enumerated special functions.
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