Generalized hypergeometric function

About: Generalized hypergeometric function is a research topic. Over the lifetime, 3678 publications have been published within this topic receiving 78332 citations.

Basic Hypergeometric Series

Abstract: Foreword Preface 1. Basic hypergeometric series 2. Summation, transformation, and expansion formulas 3. Additional summation, transformation, and expansion formulas 4. Basic contour integrals 5. Bilateral basic hypergeometric series 6. The Askey-Wilson q-beta integral and some associated formulas 7. Applications to orthogonal polynomials 8. Further applications 9. Linear and bilinear generating functions for basic orthogonal polynomials 10. q-series in two or more variables 11. Elliptic, modular, and theta hypergeometric series Appendices References Author index Subject index Symbol index.

An introduction to the mathematics and methods of astrodynamics

Abstract: Part 1 Hypergeometric Functions and Elliptic Integrals: Some Basic Topics In Analytical Dynamics The Problem of Two Bodies Two-Body Orbits and the Initial-Value Problem Solving Kepler's Equation Two-Body Orbital Boundary Value Problem Solving Lambert's Problem Appendices Part 2 Non-Keplerian Motion: Patched-Conic Orbits and Perturbation Methods Variation of Parameters Two-Body Orbital Transfer Numerical Integration of Differential Equations The Celestial Position Fix Space Navigation Appendices

Special functions of mathematical physics : a unified introduction with applications

Abstract: 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"

Generalized hypergeometric functions

Abstract: 1. The Gauss Function 2. The Generalized Gauss Function 3. Basic Hypergeometric Functions 4. Hypergeometric Integrals 5. Basic Hypergeometric Integrals 6. Bilateral Series 7. Basic Bilateral Series 8. Appell Series 9. Basic Appell Series.

Generalized Hypergeometric Series

Abstract: This also gives in the paper T. H. Koornwinder, Orthogonal polynomials with weight function (1− x)α(1 + x)β + Mδ(x + 1) + Nδ(x− 1), Canad. Math. Bull. 27 (1984), 205–214 the identitity (2.5) with N = 0 and formulas (5.3), (5.4) substituted. p.95, §10.4, formula (7): second line: replace in denominator (v + n− 1)(w + n− 1) by Γ(v + n− 1)Γ(w + n− 1); third line: replace in denominator Γ(v + n− 1) by (v + n− 1); fifth line: replace in denominator Γ(w + n− 1) by (w + n− 1).