The following corrections and other changes have been made in the DLMF, and are pending for the Handbook of Mathematical Functions. The Editors thank the users who have contributed to the accuracy of the DLMF Project by submitting reports of possible errors. For confirmed errors, the Editors have made the corrections listed here.
Several minor improvements were made affecting display and layout; primarily tracking changes to the underlying LaTeXML system.
Reported 2011-08-10 by Michael Somos.
The condition for the validity of (8.17.5) is that and are positive integers and . Previously, no conditions were stated.
Reported 2011-03-23 by Stephen Bourn.
Originally this coefficient was given incorrectly as . The other coefficients in this equation have not been changed.
Reported 2012-05-11 by Antony Lee.
The condition for the validity of this equation is . Originally it was given incorrectly as .
Originally it was stated, incorrectly, that is real when and . This statement is true only for and .
Reported 2012-07-18 by Hans Volkmer and Howard Cohl.
Originally the vector was given incorrectly as .
Reported 2012-08-27 by Klaas Vantournhout.
The entire original content of this subsection has been replaced by a reference.
The captions for these figures have been corrected to read, in part, “as a function of ” (instead of ). Also, the resolution of the graph in Figure 22.3.22 was improved near .
Reported 2011-10-30 by Paul Abbott.
Originally the denominator was given incorrectly as .
Reported 2012-02-16 by James D. Walker.
This equation is true only for . Previously, was also allowed.
Reported 2012-05-14 by Vladimir Yurovsky.
Originally this equation was given incorrectly as
Reported 2011-09-05 by Suresh Govindarajan.
Bibliographic citations were added in §§5.5(iii), 5.6(i), 5.10, 5.21, 7.13(ii), 10.19(iii), 10.21(i), 10.21(iv), 10.21(xiii), 10.21(xiv), 10.42, 10.46, 10.74(vii), 13.8(ii), 13.9(i), 13.9(ii), 13.11, 13.29(iv), 14.11, 15.13, 15.19(i), 17.18, 18.16(ii), 18.16(iv), 18.26(v), 19.12, 19.36(iv), 20.7(i), 20.7(ii), 25.11(iv), 25.18(i), 28.24, 28.34(ii), 29.20(i), 31.17(ii), and 32.17.
Other minor changes were made in the bibliography and index.
Several minor improvements were made affecting display of math and graphics on the web site; the software index and help files were updated.
Originally the left-hand side was given correctly as ; the equation is true also for .
Several minor improvements were made affecting display on the web site; the help files were revised.
The formulas in these subsections are valid only for . No conditions on were given originally.
Reported 2010-10-18 by Andreas Kurt Richter.
Originally the ordinate labels 2 and 4 in this figure were placed too high.
Reported 2010-11-08 by Wolfgang Ehrhardt.
Originally the argument to in this equation was incorrect (, rather than ), and the condition on was too weak (, rather than ). Also, the factor multiplying was rewritten to clarify the poles; originally it was .
Reported 2010-11-02 by Alvaro Valenzuela.
Originally the differential was identified incorrectly as ; the correct differential is .
The coefficient for in the first row of this table originally omitted the parentheses and was given as , instead of .
Reported 2010-09-16 by Kendall Atkinson.
Originally it was implied that is an elliptic integral. It was clarified that is an elliptic integral iff the stated conditions hold; originally these conditions were stated as sufficient but not necessary. In particular, does not satisfy these conditions.
Originally the limiting form for in the last line of this table was incorrect (, instead of ).
Originally this equation appeared with the upper limit of integration as , rather than .
Reported 2010-07-08 by Charles Karney.
Originally this equation appeared with in the summation, instead of .
Reported 2010-11-07 by Layne Watson.
Originally this equation appeared with in the second term, rather than .
The definition of the notation was added in Common Notations and Definitions.
The general references for each chapter were inserted under the i-symbol on the chapter title pages. Originally these appeared only in the References sections of the individual chapters in the Handbook.
The definition of was revised in Notations.
Additions and revisions were made in the Cross Index for Computing Special Functions.
The Handbook of Mathematical Functions was published, and the Digital Library of Mathematical Functions was released.