                                 Q: Have these formulas been verified? The results presented here have all been verified with Mathematica to be generically correct. In many cases it is possible to simply evaluate an equation in Mathematica, either by entering it directly or by applying the command FullSimplify. In:= Sin[2x] == 2Cos[x]Sin[x] Out= True When it is not possible to verify the formulas directly this way, we have verified them analytically, using our knowledge of the properties of the functions involved to select test points intelligently, evaluate the expressions using Mathematica's arbitrary-precision numerical capabilities and then verify agreement to a very high level of precision.

 Q: What does it mean to say that the results here are "generically correct"? For example, Mathematica evaluates the expression x/x == 1 to be True. However, the equation fails when x = 0 since the value of 0/0 is indeterminate. Since the equation is valid over the finite complex plane but invalid at a single point, the result is said to be generically correct. In general, an equation that is "generically correct" in will fail only in a domain of dimension n–1 or smaller.

 Q: How do I cite from this site a formula that I have used in a publication? We have recommended a citation format. Using this format will ensure that the citation remains valid through time, even if the position of a given formula within its section or subsection changes as new formulas are added.

 Q: What do you mean by InputForm and StandardForm? InputForm and StandardForm are two standardized notations used by the Mathematica system. Formulas are presented here in these two forms. InputForm expressions contain only the characters available on a standard ASCII keyboard. Expressions in InputForm can be typed directly into the Mathematica system without the use of any special key sequences. StandardForm notation is a refinement of traditional notation with certain ambiguities removed. Expressions in StandardForm can use special mathematical characters and positioning. StandardForm is the default notation used in Mathematica notebooks. However, entering some expressions in StandardForm requires the use of special keyboard commands for positioning subexpressions or entering special symbols. Here is an expression in InputForm. Integrate[1/x^2, {t, 0, 1}] Here is the same expression in StandardForm. `` `` For more information about notation in Mathematica, see Forms of Input and Output, in the Documentation Center.

 Q: Why can I only download the graphics Mathematica code that generates the graphics, instead of the graphics themselves? An evaluated notebook that contains all visualizations for a single function has an average size of about 300 MB (the size of the notebooks of some functions approaches up to 1 GB). Even when all the Postscript graphics are replaced by bitmap graphics, the average size of the notebooks is about 15 MB. Downloading such large documents is not practical. But each of the visualization notebooks can be easily evaluated and will produce all the graphics shown on the web pages. Mathematica can also export these graphics in various formats.

 Q: I would like to use some of the graphic images on this site for my teaching. How do I get permission? You may use the screen-resolution images simply by copying them, as long as the copyright notice remains. If you would like higher-resolution renditions for use in publications, please contact permissions@wolfram.com.

 Q: I'm not familiar with some of the notations used on this site. What does mean? What does mean? What does mean? In some cases, we have created new compact notations for mathematical properties like branch cuts, discontinuity sets and domains of definition. These notations are described in a separate file on this site.

 Q: This site would be more effective if it were presented using MathML, an extension to HTML for describing mathematical expressions. Do you plan on including MathML in future versions of this site? Yes, we do, as soon as there is widespread browser support for rendering MathML expressions. Mathematica's command HTMLSave already allows for the automatic generation of MathML code for mathematical expressions. The technological barrier at present is the lack of MathML support in the major browsers.

 Q: Can I mirror this site onto a local server for my university or research institution? No, you can't. Wolfram Research is hosting this free site as a service to the mathematics and science community but retains the rights to all files within it.

 Q: This site was generated from Mathematica notebooks. How can I get a copy of these source notebooks for my own use? The notebooks from which this site is generated include additional data needed to construct and update the site, and we will not release these source notebooks in their raw form.

 Q: I have a formula or fact that belongs on this site. How do I have it added? Send it to comments@functions.wolfram.com.

 Q: I've found a typo/error/bug. How can I report it? Please send it by email to comments@functions.wolfram.com.