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1: About MathML

… ►In rare cases, a browser lacks both MathML support and a robust enough javascript implementation capable of running MathJax; you may wish to visit the Customize DLMF page and choose the HTML+images document format. … ►A good resource for finding and installing math fonts is at Fonts for MathML.

2: Need Help?

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• How do I search within DLMF? See Guide to Searching the DLMF.

• See also the Index or Notations sections.

• Links to definitions, keywords, annotations and other interesting information can be found in the Info boxes by clicking or hovering the mouse over the icon next to each formula, table, figure, and section heading.

3: Guide to Searching the DLMF

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Table 1: Query Examples

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Query	Matching records contain
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int adj sin	$\int$ immediately followed by $\sin$ without any intervening terms.
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… ►Therefore, if your query is Ai^2+Bi^2, the system modifies the query so it will find the equations containing the latter expressions. … ►To find more effectively the information you need, especially equations, you may at times wish to specify what you want with descriptive words that characterize the contents but do not occur literally. …

4: How to Cite

… ►If you mention a specific equation (or chapter, section, …), you’ll help your readers find it by using our Permalinks & Reference numbers. … ►The following table outlines the correspondence between reference numbers as they appear in the Handbook, and the URL’s that find the same item online. …

5: 27.19 Methods of Computation: Factorization

… ►Deterministic algorithms are slow but are guaranteed to find the factorization within a known period of time. … ►Type II probabilistic algorithms for factoring $n$ rely on finding a pseudo-random pair of integers $(x,y)$ that satisfy $x^2\equiv y^2(modn)$. …

6: 27.16 Cryptography

… ►Applications to cryptography rely on the disparity in computer time required to find large primes and to factor large integers. … ►Procedures for finding such primes require very little computer time. …

7: 29.19 Physical Applications

… ►Macfadyen and Winternitz (1971) finds expansions for the two-body relativistic scattering amplitudes. …

8: 19.14 Reduction of General Elliptic Integrals

… ►It then improves the classical method by first applying Hermite reduction to (19.2.3) to arrive at integrands without multiple poles and uses implicit full partial-fraction decomposition and implicit root finding to minimize computing with algebraic extensions. …

9: 27.13 Functions

… ►This problem is named after Edward Waring who, in 1770, stated without proof and with limited numerical evidence, that every positive integer $n$ is the sum of four squares, of nine cubes, of nineteen fourth powers, and so on. Waring’s problem is to find, for each positive integer $k$, whether there is an integer $m$ (depending only on $k$) such that the equation …

10: 20.14 Methods of Computation

… ►For instance, to find ${\theta }_3(z,0.9)$ we use (20.7.32) with $q=0.9={\mathrm{e}}^{\mathrm{i}\pi \tau }$, $\tau =-\mathrm{i}\ln \left(0.9\right)/\pi$. …