# A Guide to Mathematical Tables

### Supplement No. 1

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No minimum order## Description

A Guide to Mathematical Tables is a supplement to the Guide to Mathematical Tables published by the U.S.S.R. Academy of Sciences in 1956. The tables contain information on subjects such as powers, rational and algebraic functions, and trigonometric functions, as well as logarithms and polynomials and Legendre functions. An index listing all functions included in both the Guide and the Supplement is included. Comprised of 15 chapters, this supplement first describes mathematical tables in the following order: the accuracy of the table (that is, the number of decimal places or significant figures); the limits of variation of the argument and the interval of the table; and the serial number of the book or journal in the reference material. The second part gives the author, title, publishing house, and date and place of publication for books, and the name of the journal, year of publication, series, volume and number, page and author and title of the article cited for journals. Topics range from exponential and hyperbolic functions to factorials, Euler integrals, and related functions. Sums and quantities related to finite differences are also tabulated. This book will be of interest to mathematicians and mathematics students.

## Table of Contents

Foreword

Index to the Tables of Contents in the Handbook and the Supplement

Part One Description of the Tables

Chapter 1. Powers, Rational and Algebraic Functions

Positive Whole Powers

Fractional Positive Powers

Roots of Fourth Power 4√n

General Fractional Powers nx

Reciprocal Values (General Whole & Fractional Powers)

Rational Functions

Algebraic Functions

Complex Numbers and their Powers

Chapter 2. Trigonometric Functions. Various Values Connected with the Circle and the Sphere

Natural Values of Trigonometric Functions

Various Expressions Containing Trigonometric Functions

Derivatives & Powers of Trigonometric Functions

Reciprocal Trigonometric Functions of a Complex Variable

Geometric Quantities

Chapter 3. Exponential and Hyperbolic Functions

Exponential Functions

Hyperbolic Functions

Expressions Containing Trigonometric and Hyperbolic Functions

Inverse Hyperbolic Functions

Chapter 4. Logarithms

Common Logarithms and Antilogarithms

Natural Logarithms

Logarithms with Base 2

Chapter 5. Factorials, Euler Integrals & Related Functions

Factorials

The Gamma Function

The Psi Function & its Derivatives

The Beta Function

Certain Constants

Chapter 6. Sine and Cosine Integrals, Exponential and Logarithmic Integrals and Related Functions

Sine and Cosine Integral

Hyperbolic Sine and Cosine Integrals

Exponential Integral

Logarithmic Integral

Generalised & Mixed Integral Functions

Integral Functions for Complex Arguments

Chapter 7. Probability Integrals and Related Functions

Probability Distribution and Related Functions

Probability Integrals and Expressions Containing Them

Various Integrals

Tables in which the Integral Serves as the Argument

Probability Integrals with Complex Argument

Derivatives of Various Orders of Distribution Function

Zeros of Probability Integrals

Logarithms of Probability Integrals

Fresnel Integrals & Related Functions

Chapter 8. Elliptic Integrals and Functions

Moduli of the Integrals

Complete Elliptic Integrals

Incomplete Elliptic Integrals

Elliptic Functions

Theta Functions

Chapter 9. Legendre Functions and Polynomials

Legendre Functions and Polynomials of the First Kind

Associated Legendre Functions of the First Kind

Roots of Legendre Functions

Various Expressions Containing Legendre Functions

Chapter 10. Cylinder Functions

Cylinder Functions of the First & Second Kind of Real Argument

Riccati-Bessel Functions

Lommel's Functions of Two Real Variables

Cylinder Functions of the Third Kind (Hankel Functions)

Cylinder Functions of the First & Second Kind of Imaginary Argument

Lommel's Functions of Two Imaginary Variables

Cylinder Functions of Complex Argument

Thomson Functions

Airy Functions

A Special Confluent Hypergeometric Function

Struve Functions

Zeros of Cylinder Functions

Integrals of Cylinder Functions

Chapter 11. Certain Special Functions & Integrals

Polynomials

Riemann Zeta Function

Mathieu Functions

Hypergeometric & Confluent Hypergeometric Functions

Whittaker Functions

Functions of a Parabolic Cylinder (Weber Functions)

Certain Integrals

Various Functions

Chapter 12. Solutions of Certain Equations

Algebraic Equations

Equations Containing Trigonometric Functions

Equations Containing Exponential Functions

Various Equations

Solutions of Differential Equations

Solutions of Integral Equations

Chapter 13. Sums & Values Connected with Finite Differences

Binomial Coefficients

Interpolation Coefficients

Numerical Differentiation and Integration

Sums

Chapter 14. Mathematical Constants

Chapter 15. Prime Numbers, Factors, Products, Quotients and Fractions

Conversion from One System of Calculation to Another

Part Two References

References to Chapter 1 (Powers, Rational & Algebraic Functions)

References to Chapter 2 (Trigonometric Functions. Various Quantities Connected with the Circle and the Sphere)

References to Chapter 3 (Exponential & Hyperbolic functions)

References to Chapter 4 (Logarithms)

References to Chapter 5 (Factorials, Euler Integrals and Related Functions)

References to Chapter 6 (Sine and Cosine Integrals, Exponential and Logarithmic Integrals and Related Functions)

References to Chapter 7 (Probability Integrals and Related Functions)

References to Chapter 8 (Elliptic Integrals and Elliptic Functions)

References to Chapter 9 (Legendre Functions and Polynomials)

References to Chapter 10 (Cylinder Functions)

References to Chapter 11 (Certain Special Functions and Integrals)

References to Chapter 12 (Solutions of Certain Equations)

References to Chapter 13 (Sums and Quantities Connected with Finite Differences)

References to Chapter 14 (Mathematical Constants)

References to Chapter 15 (Prime Numbers, Factors, Products, Quotients and Fractions)

Author Index

Supplement. Translated Titles from the Reference Section

## Product details

- No. of pages: 234
- Language: English
- Copyright: © Pergamon 1960
- Published: January 1, 1960
- Imprint: Pergamon
- eBook ISBN: 9781483184432

## About the Authors

### N. M. Burunova

### A. V. Lebedev

### R. M. Fedorova

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