Book:Ephraim J. Borowski/Dictionary of Mathematics

Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics

Published $\text {1989}$, Collins Reference

ISBN 0-00-434347-6.

Subject Matter

Mathematics

Errata

Sum of Infinite Geometric Sequence

geometric series

The sum of the finite initial segments of the series is:

$\dfrac {a \paren {r^n - 1} } {r - 1}$,

whence, if the infinite series converges, its sum is $a / \paren {r - 1}$.

Lucas Numbers

Lucas numbers

the sequence of integers

$2, 1, 3, 4, 7, 11, 18, 29, \dotsc$

derived from the same difference equation as the fibonacci numbers, but using different initial values. (Named after the English mathematician Henry Lucas (died 1663).)

Octal

octal

... for example, $371.24_8$ represents the number

$\paren {3 \times 8^2} + \paren {7 \times 8^1} + \paren {1 \times 8^0} + \paren {2 \times 8^{-1} } + \paren {4 \times 8^{-2} } = 249.25_{10}$.

Pentagonal Number

pentagonal number

a figurate number of the form $n \paren {3 n \pm 1}$.

Primitive of Reciprocal

Appendix $2$: Table of derivatives and integrals of common functions

$\ds \map f x: \, $

$\ds $

$\ds x^{-1}$

$\ds \int \map f x \rd x: \, $