NIST Handbook of Mathematical Functions

NIST Handbook of Mathematical Functions

by Frank W. J. Olver
     
 

ISBN-10: 0521140633

ISBN-13: 9780521140638

Pub. Date: 05/10/2010

Publisher: Cambridge University Press

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. Thes functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in

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Overview

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. Thes functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties.&;lt;BR&;gt;&;lt;BR&;gt;This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. It is destined to replace its predecessor, the classic but long-outdated NBS Handbook of Mathematical Functions, edited by Abramowitz and Stegun.

Product Details

ISBN-13:
9780521140638
Publisher:
Cambridge University Press
Publication date:
05/10/2010
Pages:
968
Sales rank:
680,941
Product dimensions:
8.50(w) x 10.90(h) x 2.00(d)

Table of Contents

Foreword

Preface

Mathematical Introduction

1 Algebraic and Analytic Methods R. Wong Wong, R. 1

2 Asymptotic Approximations R. Wong Wong, R. 41

3 Numerical Methods N. M. Temme Temme, N. M. 71

4 Elementary Functions F. W. J. Olver Olver, F. W. J. 103

5 Gamma Function R. Roy Roy, R. 135

6 Exponential, Logarithmic, Sine, and Cosine Integrals N. M. Temme Temme, N. M. 149

7 Error Functions, Dawson's and Fresnel Integrals N. M. Temme Temme, N. M. 159

8 Incomplete Gamma and Related Functions R. B. Paris Paris, R. B. 173

9 Airy and Related Functions F. W. J. Olver Olver, F. W. J. 193

10 Bessel Functions L. C. Maximon Maximon, L. C. 215

11 Struve and Related Functions R. B. Paris Paris, R. B. 287

12 Parabolic Cylinder Functions N. M. Temme Temme, N. M. 303

13 Confluent Hypergeometric Functions A. B. Olde Daalhuis Daalhuis, A. B. Olde 321

14 Legendre and Related Functions T. M. Dunster Dunster, T. M. 351

15 Hypergeometric Function A. B. Olde Daalhuis Daalhuis, A. B. Olde 383

16 Generalized Hypergeometric Functions and Meijer G-Function A. B. Olde Daalhuis Daalhuis, A. B. Olde 403

17 q-Hypergeometric and Related Functions G. E. Andrews Andrews, G. E. 419

18 Orthogonal Polynomials R. F. Swarttouw Swarttouw, R. F. 435

19 Elliptic Integrals B. C. Carlson Carlson, B. C. 485

20 Theta Functions P. L. Walker Walker, P. L. 523

21 Multidimensional Theta Functions B. Deconinck Deconinck, B. 537

22 Jacobian Elliptic Functions P. L. Walker Walker, P. L. 549

23 Weierstrass Elliptic and Modular Functions P. L. Walker Walker, P. L. 569

24 Bernoulli and Euler Polynomials K. Dilcher Dilcher, K. 587

25 Zeta and Related Functions T. M. Apostol Apostol, T. M. 601

26 Combinatorial Analysis D. M. Bressoud Bressoud, D. M. 617

27 Functions of Number Theory T. M. Apostol Apostol, T. M. 637

28 Mathieu Functions and Hill's Equation G. Wolf Wolf, G. 651

29 Lame Functions H. Volkmer Volkmer, H. 683

30 Spheroidal Wave Functions H. Volkmer Volkmer, H. 697

31 Heun Functions V. B. Kuznetsov Kuznetsov, V. B. 709

32 Painleve Transcendents P. A. Clarkson Clarkson, P. A. 723

33 Coulomb Functions I. J. Thompson Thompson, I. J. 741

34 3j, 6j, 9j Symbols L. C. Maximon Maximon, L. C. 757

35 Functions of Matrix Argument D. St. P. Richards Richards, D. St. P. 767

36 Integrals with Coalescing Saddles C. J. Howls Howls, C. J. 775

Bibliography 795

Notations 873

Index 887

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