Tables

• I. N. Bronshtein
• K. A. Semendyayev

Abstract

Interpolation. Most of the tables inserted below give the values of functions to four significant figures for three significant figures of the argument. In the cases, when the argument is given with a greater accuracy, and the desired value of the function cannot be obtained directly from the tables, interpolation should be used. The simplest form is linear interpolation in which we assume that the increment of the function is proportional to the increment of the argument. If the desired value of the argument x lies between the values x0 and x1 = x0 + h in the tables and the corresponding values of the function are
$$y_{0}=f(x_{0})\;\;\;\textup{and}\;\;\;y_{1}=f(x_{1})=y_{0}+\mathit{\Delta}$$
, then we assume that
$$f(x)=f(x_{0})+\frac{x-x_{0}}{h}\mathit{\Delta}$$
.

Keywords

Significant Figure Linear Interpolation Trigonometric Function Figure Group Cube Root
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

1. (1).
The difference Δ is usually expressed in the units of the last order of the value of the function, without the first zeros or the decimal point.Google Scholar
2. (1).
It is better to write 1793 =5.735 · 106 avoiding unnecessary zeros put instead of unknown figures (exactly, 1793=5735339).Google Scholar
3. (1).
Zero at the end should be preserved, for it is a significant figure and indicates the accuracy of the obtained value of the root.Google Scholar
4. (1).
The number y whose common logarithm is equal to x is called the antilogarithm of x. By definition of the logarithm (see p. 156), this function coincides with the exponential function y = 10x.Google Scholar
5. (1).
For the corresponding formulas see pp. 200, 201.Google Scholar
6. (1).
For definitions and graphs see pp. 551, 552.Google Scholar
7. (1).
Definitions are given on pp. 407, 408Google Scholar
8. (1).
The graph of Φ(x) and some applications of it are given on pp. 747, 748. Sometimes the function $$\textup{Erf}\;x=\frac{2}{\sqrt{\pi} }\int\limits_{0}^{x}e^{-t}dt^{2}=\mathit{\Phi} (x\sqrt{2})$$ is called the probability integral.Google Scholar