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

Contents

Preface
Dictionary of Mathematics
Appendix 1: Symbols and Conventions
Appendix 2: Table of Derivatives and Integrals
Appendix 3: Hilbert Problems

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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

 $\ds \map f x: \,$ $\ds$  $\ds x^{-1}$ $\ds \int \map f x \rd x: \,$ $\ds$  $\ds \ln x$