Table of Integrals, Series, and Products Seventh Edition
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Table of Integrals, Series, and Products Seventh Edition
I.S. Gradshteyn and I.M. Ryzhik Alan Jeffrey, Editor University of Newcastle upon Tyne, England
Daniel Zwillinger, Editor Rensselaer Polytechnic Institute, USA
Translated from Russian by Scripta Technica, Inc.
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Contents Preface to the Seventh Edition Acknowledgments The Order of Presentation of the Formulas Use of the Tables Index of Special Functions Notation Note on the Bibliographic References 0
Introduction 0.1 0.11 0.12 0.13 0.14 0.15 0.2 0.21 0.22 0.23–0.24 0.25 0.26 0.3 0.30 0.31 0.32 0.33 0.4 0.41 0.42 0.43 0.44
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xxi xxiii xxvii xxxi xxxix xliii xlvii
Finite Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sums of powers of natural numbers . . . . . . . . . . . . . . . . Sums of reciprocals of natural numbers . . . . . . . . . . . . . . Sums of products of reciprocals of natural numbers . . . . . . . Sums of the binomial coefficients . . . . . . . . . . . . . . . . . Numerical Series and Infinite Products . . . . . . . . . . . . . . The convergence of numerical series . . . . . . . . . . . . . . . Convergence tests . . . . . . . . . . . . . . . . . . . . . . . . . Examples of numerical series . . . . . . . . . . . . . . . . . . . Infinite products . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of infinite products . . . . . . . . . . . . . . . . . . . Functional Series . . . . . . . . . . . . . . . . . . . . . . . . . . Definitions and theorems . . . . . . . . . . . . . . . . . . . . . . Power series . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fourier series . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asymptotic series . . . . . . . . . . . . . . . . . . . . . . . . . . Certain Formulas from Differential Calculus . . . . . . . . . .