With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan� tum mechanics. We have not attempted to provide the most extensive collec� tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro� vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (�3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (��12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or� thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications in physics.

Contenuti

I Foundations of the theory of special functions.- II The classical orthogonal polynomials.- III Bessel functions.- IV Hypergeometric functions.- V Solution of some problems of mathematical physics, quantum mechanics and numerical analysis.- Appendices.- A. The Gamma function.- B. Analytic properties and asymptotic representations of Laplace integrals.- Basic formulas.- List of tables.- References.- Index of notations.- List of figures.

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