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Errata for
Standard Mathematical Tables and Formulae (31st edition)

by Daniel Zwillinger (Editor-in-chief)
(Boca Raton, Florida: CRC Press, 2003) 910pp. ISBN 1-58488-291-3

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LAST UPDATED: May 23, 2004


NOTES:

  1. Due to our procedures for verifying errata, the date that an entry is updated may be significantly later than the date that the errata was brought to our attention.

  2. Sometimes many contributors bring the same errata to our attention.

  3. The .pdf version of this errata list include an index of dates of when the errata were updated.

  4. The latest errata is available from http://www.mathtable.com/errata/.

ERRATA:

  1. NEGATIVE INTEGER POWERS, 1.2.12, 24. Some of the values of the zeta function are incorrect:
    expression   old incorrect value   correct value
    $ \zeta(2)$   1.644934066\fbox{9}   1.644934066\fbox{8}
    $ \zeta(10)$   1.000994575\fbox{2}   1.000994575\fbox{1}
    $ \zeta(14)$   1.000061248\fbox{2}   1.000061248\fbox{1}

    (Thanks to Harvey P. Dale for correcting this error.)

    This entry last updated 23 May 2004.

  2. REGULAR POLYGONS, 4.5.3, 276. Presently the book has

    \begin{displaymath}\begin{split}\textrm{area}&=\frac{1}{4}ka^2\cot\frac{180^{\ci... ...aystyle \frac{1}{2}kR^2\sin\frac{360^{\circ}}{k}$}, \end{split}\end{displaymath}    

    This is incorrect, it should have been:

    \begin{displaymath}\begin{split}\textrm{area}&=\frac{1}{4}ka^2\cot\frac{180^{\ci... ...tyle \frac{s^2}{k}\cot\frac{360^{\circ}}{k} = rs$}, \end{split}\end{displaymath}    

    (Thanks to John W. Dyer for correcting this error.)

    This entry last updated 23 May 2004.

  3. Spherical half angle formulae, 4.19.2.5, 370. The expression `` $ (\tan r)^2$'' in the first line should be removed since $ r$ is not defined in this section.

    (Thanks to Michael Pender for correcting this error.)

    This entry last updated 23 May 2004.

  4. Spherical half angle formulae, Section 4.19.2.6, 371 The expression `` $ (\tan R)^2$'' in the first line should be removed since $ R$ is not defined in this section.

    This entry last updated 23 May 2004.

  5. MOMENTS OF INERTIA FOR VARIOUS BODIES, Section 5.3.12, 410. The definition of the moment of inertia is missing. The following line should be added:

    moment of intertia$\displaystyle =\int_A r^2\,dA$

    (Thanks to Mike Strauss for correcting this error.)

    This entry last updated 23 May 2004.

  6. INTEGRALS, Section 6.19.7, 410. This section would be better named INTEGRAL REPRESENATIONS.

    This entry last updated 23 May 2004.

  7. Integral 631, Section 5.5, 451. The evaluation of the integral is given as
    $ \displaystyle \frac{1}{2} B \left( \frac{n}{2} \right) \frac{m}{2} $
    which is incorrect, it should have been
    $ \displaystyle \frac{1}{2} B \left( \frac{n}{2}, \frac{m}{2} \right) $

    (Thanks to Roger Nelsen for correcting this error.)

    This entry last updated 23 May 2004.

    FOOTNOTE: An alert reader will wonder how this error could have occurred, since the integrals in the last edition of this book have been electronically verified. The error occurred in the typesetting of this integral--not in the electronic verification of the integrals.

  8. Integral 635, Section 5.5, 451. The constraint on the integral is presently
    $ m$ is a non-negative integer
    which is correct; but could be expanded to
    $ m$ is real

    (Thanks to Roger Nelsen for correcting this error.)

    This entry last updated 23 May 2004.

  9. Section 6.3.2, 518. The displayed equation now has

    $\displaystyle t$ $\displaystyle =\arcsin{z}=(-1)^k t_0 + k\pi,$ with $ \sin t_0=z$$\displaystyle ,$    
    $\displaystyle t$ $\displaystyle =\arccos{z}= \pm t_1 + 2k\pi,$ with $ \fbox{$\sin$} t_1=z$$\displaystyle ,$    
    $\displaystyle t$ $\displaystyle =\arctan{z}= t_2 + k\pi,$ with $ \fbox{$\sin$} t_2=z$$\displaystyle ,$    

    which is incorrect; it should be

    $\displaystyle t$ $\displaystyle =\arcsin{z}=(-1)^k t_0 + k\pi,$ with $ \sin t_0=z$$\displaystyle ,$    
    $\displaystyle t$ $\displaystyle =\arccos{z}= \pm t_1 + 2k\pi,$ with $ \fbox{$\cos$} t_1=z$$\displaystyle ,$    
    $\displaystyle t$ $\displaystyle =\arctan{z}= t_2 + k\pi,$ with $ \fbox{$\tan$} t_2=z$$\displaystyle ,$    

    (Thanks to Timothy Leung for correcting this error.)

    This entry last updated 23 May 2004.

  10. Formula 6.21.2 3, Section 6.21.2, 573. The formula is presently
    $ \frac{d {}}{d {u} } {\mathrm{dn}}u = -k^2 {\mathrm{cn}}u {\mathrm{dn}}u$.
    This is incorrect; it should have been
    $ \frac{d {}}{d {u} } {\mathrm{dn}}u = -k^2 {\mathrm{cn}}u {\mathrm{sn}}u$.

    (Thanks to Jesse Pratt for correcting this error.)

    This entry last updated 23 May 2004.

  11. LAPLACE TRANSFORMS, Section 6.33, 607. Entries number 29 and 30 are presently:

    No. $ f(t)$ $ F(s)$
    29 $ -\frac{e^{\fbox{\scriptsize$-$}at}}{4^{n-1}b^{2n}}\sum_{k=1}^n \binom{2n-k-1}{n-1}$
    $ \times \fbox{$(-2t)^{k-1}$} \frac{d^{k} {}}{d {t}^{k}} [\cos bt]$    		 $ \displaystyle \frac{1}{ \left[ (s-a)^2+b^2 \right] ^n}$
    30 $ \frac{e^{\fbox{\scriptsize$-$}at}}{4^{n-1}b^{2n}} \Big\{ \sum_{k=1}^n \binom{2n-k-1}{n-1} \frac{(-2t)^{k-1}}{(k-1)!}$
         $ \times \frac{d^{k} {}}{d {t}^{k}} \left[ a\cos bt+b\sin \fbox{$a$}t \right] $
         $ - 2b \sum_{k=1}^{n-1} \binom{2n-k-2}{n-1} \frac{(-2t)^{k-1}}{(k-1)!}$
         $ \times \frac{d^{k} {}}{d {t}^{k}} \left[ \sin bt \right] \Big\}$    		 $ \displaystyle \frac{s}{ \left[ (s-a)^2+b^2 \right] ^n}$

    These are incorrect, they should have been:

    No. $ f(t)$ $ F(s)$
    29 $ -\frac{e^{at}}{4^{n-1}b^{2n}}\sum_{k=1}^n \binom{2n-k-1}{n-1}$
    $ \times \fbox{$\frac{(-2t)^{k-1}}{(k-1)!}$} \frac{d^{k} {}}{d {t}^{k}} [\cos bt]$    		 $ \displaystyle \frac{1}{ \left[ (s-a)^2+b^2 \right] ^n}$
    30 $ \frac{e^{-at}}{4^{n-1}b^{2n}} \Big\{ \sum_{k=1}^n \binom{2n-k-1}{n-1} \frac{(-2t)^{k-1}}{(k-1)!}$
         $ \times \frac{d^{k} {}}{d {t}^{k}} \left[ \fbox{$-$}a\cos bt+b\sin \fbox{$b$}t \right] $
         $ - 2b \sum_{k=1}^{n-1} \binom{2n-k-2}{n-1} \frac{(-2t)^{k-1}}{(k-1)!}$
         $ \times \frac{d^{k} {}}{d {t}^{k}} \left[ \sin bt \right] \Big\}$    		 $ \displaystyle \frac{s}{ \left[ (s-a)^2+b^2 \right] ^n}$

    (Thanks to Ningning Song for correcting this error.)

    This entry last updated 23 May 2004.

  12. Formula 7.14.1, Section 7.14.1, 695. The integral presently has an upper limit of ``$ \infty$''; this is incorrect. The upper limit should be ``$ z$''.

    (Thanks to Joseph J. Rushanan for correcting this error.)

    This entry last updated 23 May 2004.


Errata for Standard Mathematical Tables and Formulae