MATHEMATICAL REFERENCE / AMS55

Handbook of Mathematical Functions

Abramowitz and Stegun's classic collection of formulas, graphs, and mathematical tables. Original page scans and deep links are preserved.

ChapterChoose a chapterTitle PagePrefaceForewordContentsIntroduction1. Mathematical Constants2. Physical Constants and Conversion Factors3. Elementary Analytical Methods4. Elementary Transcendental Functions Logarithmic, Exponential, Circular and Hyperbolic Functions5. Exponential Integral and Related Functions6. Gamma Function and Related Functions7. Error Function and Fresnel Integrals8. Legendre Functions9. Bessel Functions of Integer Order10. Bessel Functions of Fractional Order11. Integrals of Bessel Functions12. Struve Functions and Related Functions13. Confluent Hypergeometric Functions14. Coulomb Wave Functions15. Hypergeometric Functions16. Jacobian Elliptic Functions and ThetaFunctions17. Elliptic Integrals18. Weierstrass Elliptic and Related Functions19. Parabolic Cylinder Functions20. Mathieu Functions21. Spheroidal Wave Functions22. Orthogonal Polynomials23. Bernoulli and Euler Polynomials, Riemann Zeta Function24. Combinatorial Analysis25. Numerical Interpolation, Differentiation and Integration26. Probability Functions27. Miscellaneous Functions28. Scales of Notation29. Laplace TransformsSubject IndexIndex of Notations

Printed page (0 = contents; -1 to -14 = front matter) Go to page

Scan number (1 to 1060) Go to scan

Table of contents

Find a section in the contents

• Title Page
• Preface
• Foreword
• Contents
• Introduction
• 1. Mathematical Constants (p. 1)
• 2. Physical Constants and Conversion Factors (p. 5)
• 3. Elementary Analytical Methods (p. 9)
• 4. Elementary Transcendental Functions
  Logarithmic, Exponential, Circular and Hyperbolic Functions (p. 65)
• 5. Exponential Integral and Related Functions (p. 227)
• 6. Gamma Function and Related Functions (p. 253)
• 7. Error Function and Fresnel Integrals (p. 295)
• 8. Legendre Functions (p. 331)
• 9. Bessel Functions of Integer Order (p. 355)
• 10. Bessel Functions of Fractional Order (p. 435)
• 11. Integrals of Bessel Functions (p. 479)
• 12. Struve Functions and Related Functions (p. 495)
• 13. Confluent Hypergeometric Functions (p. 503)
• 14. Coulomb Wave Functions (p. 537)
• 15. Hypergeometric Functions (p. 555)
• 16. Jacobian Elliptic Functions and ThetaFunctions (p. 567)
• 17. Elliptic Integrals (p. 587)
• 18. Weierstrass Elliptic and Related Functions (p. 627)
• 19. Parabolic Cylinder Functions (p. 685)
• 20. Mathieu Functions (p. 721)
• 21. Spheroidal Wave Functions (p. 751)
• 22. Orthogonal Polynomials (p. 771)
• 23. Bernoulli and Euler Polynomials, Riemann Zeta Function (p. 803)
• 24. Combinatorial Analysis (p. 821)
• 25. Numerical Interpolation, Differentiation and Integration (p. 875)
• 26. Probability Functions (p. 925)
• 27. Miscellaneous Functions (p. 997)
• 28. Scales of Notation (p. 1011)
• 29. Laplace Transforms (p. 1019)
• Subject Index (p. 1031)
• Index of Notations (p. 1044)

OCR text for this page (may contain scanning errors)

Scanned text; use the page image to verify formulasXIV INTRODUCTION 8. Acknowledgments The production of this volume has been the result of the unrelenting efforts of many persons, all of whose contributions have been instrumental in accomplishing the task. The Editor expresses his thanks to each and every one. The Ad Hoc Advisory Committee individually and together were instrumental in establishing the basic tenets that served as a guide in the forma- tion of the entire work. In particular, special thanks are due to Professor Philip M. Morse for his continuous encouragement and support. Professors J. Todd and A. Erddlyi, panel members of the Conferences on Tables and members of the Advisory Committee have maintained an un- diminished interest, offered many suggestions and carefully read all the chapters. Irene A. Stegun has served effectively as associate editor, sharing in each stage of the planning of the volume. Without her untiring efforts, com- pletion would never have been possible. Appreciation is expressed for the generous cooperation of publishers and authors in granting permission for the use of their source material. Acknowledgments for tabular material taken wholly or in part from published works are given on the first page of each table. Myrtle R. Kelling- ton corresponded with authors and publishers to obtain formal permission for including their material, maintained uniformity throughout the bibliographic references and assisted in preparing the introductory material. Valuable assistance in the preparation, checkin and editing of the tabular material was receive from Ruth E. Capuano, Elizabeth F. Godefroy, David S. Liepman, Kermit Nelson, Bertha H. Walter and Ruth Zucker. Equally important has been the untiring cooperation, assistance, and patience of the members of the NBS staff in handling the myriad of detail necessarily attending the publication of a volume of this magnitude. Especially appreciated have been the helpful discussions and services from the members of the Office of Techni- cal Information in the areas of editorial format, graphic art layout, printing detail, preprinting reproduction needs, as well as attention to pro- motional detail and financial support. In addition, the clerical and typing st& of the Applied Mathe- matics Division merit commendation for their efficient and patient production of manuscript copy involving complicated technical notation. Finally, the continued support of Dr. E. W. Cannon, chief of the Applied Mathematics Division, and the advice of Dr. F. L. Alt, assistant chief, as well as of the many mathematicians in the Division, is gratefully acknowledged. % M. ABRAMOWITZ.

The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States.