Errata for
by Daniel Zwillinger (Editorinchief)

NOTE THAT THERE MAY EXIST ERRORS IN THIS PRINTING THAT WERE NOT CORRECTED IN THE NEXT PRINTING. PLEASE LOOK AT THE LIST OF ERRATA FOR LATER PRINTINGS.
n  2^{n}  n  2^{n} 
41  2199023255552  81  2417851639229258349412352 
42  4398046511104  82  4835703278458516698824704 
43  8796093022208  83  9671406556917033397649408 
44  17592186044416  84  19342813113834066795298816 
45  35184372088832  85  38685626227668133590597632 
46  70368744177664  86  77371252455336267181195264 
47  140737488355328  87  154742504910672534362390528 
48  281474976710656  88  309485009821345068724781056 
49  562949953421312  89  618970019642690137449562112 
50  1125899906842624  90  1237940039285380274899124224 
This is incorrect. It should be
This is incorrect. It should say (note )
...That is, exists. ...This is incorrect. It should say
...That is, exists. ...
(Archimedean property of ) For every real number x there is an integer N such that x < n.This is incorrect. It should say
(Archimedean property of ) For every real number x there is an integer N such that x < N.
is An orthonormal set ...This is incorrect. It should say
is An orthonormal set ...
...series is ... expressed as .This is incorrect. It should say
...series is ... expressed as .
All the known Mersenne primes, ..., 756839, 859433.This is incorrect. It should say
All the known Mersenne primes, ..., 756839, 859433, 1257787.
This should be changed to (note new top line, and addition of the word ``known''):
Number  Number of digits 
^{}378,632  
2^{859433}  1  258,716 
2^{756839}1  227,832 
^{}65,087  
2^{216091}1  65,050 
Note that the last, say, three lines of the table should be deleted.
The largest known twin primes are: (with 4,932 digits), (with 4,030 digits), and (with 3,439 digits).This is incorrect. It should say
The largest known twin primes are: (with 11,713 digits), (with 5,129 digits), and (with 4,932 digits).
3, 5, 11, 41, ...This is incorrect (there is a missing term in the sequence). It should say
3, 5, 11, 13, 41, ...
All real matrices are Hermitian.This is incorrect. It should say
All real symmetric matrices are Hermitian.
This is incorrect. It should say
This is incorrect. It should say
The characteristic polynomial has...This is incorrect. It should say (note the upper limit)
The characteristic polynomial has...
The letters P, Q, and R are used to designate compound statements.
For example, if P ...with
For example, suppose that P and Q are compound statements. Then if P ...
This is incorrect. It should say (look at the lower value in the last Stirling number)
The Stirling cycle number, , is the number of ways to partition n into k blocks. (Equivalently, it is the number of ways that n distinguishable balls can be placed in k indistinguishable cells, with no cell empty.)This is incorrect. It should say (note )
The Stirling cycle number, , is the number of ways to partition n into m blocks. (Equivalently, it is the number of ways that n distinguishable balls can be placed in m indistinguishable cells, with no cell empty.)
This is incorrect. It should say (look at the lower value in the last Stirling number)
A sequence is a degree sequence of a graph if there is some ordering of the vertices for which d_{i} is the degree of v_{i} for each i.
The numbers of ...following table:''This is incorrect and should be replaced by
The following table lists the number of isomorphism classes of graphs of order n and size m.
1 1 2 3 7 16 54 283This is incorrect. It should say
1 1 2 3 7 16 54 243
This is incorrect. It should say
A polygon is regular if all its angles are equal. This also implies that all sides are equal. (However, the sides can be equal even if the polygon is not regular, as in the case of the rhombus).This is incorrect. It should say
A polygon is regular if all its sides are equal and all its angles are equal. Either condition implies the other in the case of a triangle, but not in general. (A rhombus has equal sides but not necessarily equal angles, and a rectangle has equal angles but not necessarily equal sides.)
This is incorrect. It should say
1 1 2 3 7 21 49 166 549This is incorrect. It should say
1 1 2 3 7 21 49 165 552
...is equivalent to C^{k} regular parametric representation if an only ...This is incorrect. It should say
...is equivalent to a C^{k} regular parametric representation if and only ...
A regular curve C of class C_{k} is an equivalenceThis is incorrect. It should say
A regular curve C of class C^{k} is an equivalence
whose the real ...This is incorrect. It should say
where the real ...
This is incorrect. It should say (Note indices in first )
This is incorrect. It should say
This is incorrect. It should say
This is incorrect. It should say
This is confusing. It should be replaced by
Logarithmic expressions are to base , unless otherwise specified, and are to be evaluated for the absolute value of the arguments involved therein.
If q=0 then and ...This is incorrect. It should say
If q=0 then and ...
...This is incorrect. It should say
...
This is incorrect. It should read (Note font size in )
This is incorrect. It should read (Note subscript positioning and )
This is incorrect. It should say (note the first superscript of the first T)
This is incorrect. It should say (note the last subscript on the last T)
with respect to the conditionThis is incorrect. It should read
with respect to the connection
is said to an ...This is incorrect. It should read
is said to be an ...
is said to LorentzianThis is incorrect. It should read
is said to be Lorentzian
This is incorrect. It should read (note indices)
This is incorrect. It should read (note subscript j in R)
This is incorrect. It should read (note subscript k in second term)
This is incorrect. It should read (note subscripts on first ,and change of sign)
They are incorrect. They should read (note the sign changes on the 3rd and 4th equations)
The Laplacian of a scalar invariant f is given byThis is incorrect. It should read (note the subscript on the second )
The Laplacian of a scalar invariant f is given by
This is incorrect. It should read (there are changes in all three lines)
This is incorrect. It should read (notice the second subscript on the first O term)
x^{2}+y^{2}+z^{2}+=r^{2} ......These are incorrect. They should be
x^{2}+y^{2}+z^{2}=r^{2} ......
R=2r^{2}This is incorrect. It should read
R=2r^{2}
is incorrect. It should say
This is incorrect. It should say
DEFINITION OF THE FUNCTIONThis is incorrect. It should say
DEFINITION OF THE FFUNCTION
For example, number 9 should be f(t)=e^{at} is equivalent to .
This is incorrect (notice the t in the denominator). It should say
which is incorrect. It should be
Let S(t) represent a signal to be recovered, let N(t) represent noise, and let Y(t)=S(t)+N(t) represent the observable. A prediction of the signal is where K(z) is a filter. The mean square error is ...This is incorrect. It should say (note ):
Let X(t) represent a signal to be recovered, let N(t) represent noise, and let Y(t)=X(t)+N(t) represent the observable. A prediction of the signal is where K(z) is a filter. The mean square error is ...
which is incorrect. This should be (note the removal of one set of vertical dots in each matrix)
This is incorrect. It should say:
1cTo obtain  1cMultiply  1cBy 
Inches  Centimeters  
Feet  Meters  3.280840 
Yards  Meters  1.093613 
Miles  Kilometers  0.6213712 
Ounces  Grams  
Pounds  Kilograms  2.204623 
Gallons (US)  Liters  0.2641721 
Fluid ounces  Milliliters (cc)  
Square inches  Square centimeters  0.1550003 
Square feet  Square meters  10.76391 
Square yards  Square meters  1.195990 
Cubic inches  Milliliters (cc)  
Cubic feet  Cubic meters  35.31467 
Cubic yards  Cubic meters  1.307951 
1cTo obtain  1cMultiply  1cBy 
Microns  Mils  25.4 
Centimeters  Inches  2.540000 
Meters  Feet  0.3048000 
Meters  Yards  0.9144000 
Kilometers  Miles  1.609344 
Grams  Ounces  28.34952 
Kilograms  Pounds  0.4535924 
Liters  Gallons (US)  3.785412 
Milliliters (cc)  Fluid ounces  29.57353 
Square centimeters  Square inches  6.451600 
Square meters  Square feet  0.09290304 
Square meters  Square yards  0.8361274 
Milliliters (cc)  Cubic inches  16.38706 
Cubic meters  Cubic feet  
Cubic meters  Cubic yards  0.7645549 
These are correct as written, but several users misread the column captions. I recommend that the order of the columns be changed, and that the terms in exponential notation be changed, to obtain:
1cMultiply  1cBy  1cTo obtain 
Centimeters  0.3937008  Inches 
Meters  3.280840  Feet 
Meters  1.093613  Yards 
Kilometers  0.6213712  Miles 
Grams  0.03527396  Ounces 
Kilograms  2.204623  Pounds 
Liters  0.2641721  Gallons (US) 
Milliliters (cc)  0.03381402  Fluid ounces 
Square centimeters  0.1550003  Square inches 
Square meters  10.76391  Square feet 
Square meters  1.195990  Square yards 
Milliliters (cc)  0.06102374  Cubic inches 
Cubic meters  35.31467  Cubic feet 
Cubic meters  1.307951  Cubic yards 
1cMultiply  1cBy  1cTo obtain 
Mils  25.4  Microns 
Inches  2.540000  Centimeters 
Feet  0.3048000  Meters 
Yards  0.9144000  Meters 
Miles  1.609344  Kilometers 
Ounces  28.34952  Grams 
Pounds  0.4535924  Kilograms 
Gallons (US)  3.785412  Liters 
Fluid ounces  29.57353  Milliliters (cc) 
Square inches  6.451600  Square centimeters 
Square feet  0.09290304  Square meters 
Square yards  0.8361274  Square meters 
Cubic inches  16.38706  Milliliters (cc) 
Cubic feet  0.02831685  Cubic meters 
Cubic yards  0.7645549  Cubic meters 