Author | Nikiforov, Arnold F. author |
---|---|

Title | Special Functions of Mathematical Physics [electronic resource] : A Unified Introduction with Applications / by Arnold F. Nikiforov, Vasilii B. Uvarov |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1988 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-1595-8 |

Descript | XVIII, 427 p. online resource |

SUMMARY

With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quanยญ tum mechanics. We have not attempted to provide the most extensive collecยญ 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 proยญ 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 (ยง3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (ยงยง12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical orยญ 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

CONTENT

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

Mathematics
Special functions
Applied mathematics
Engineering mathematics
Physics
Mathematics
Special Functions
Applications of Mathematics
Mathematical Methods in Physics