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1: 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.

2: 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. …

3: 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 $x^2\equiv y^2(modn)$. …

4: 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. …

5: 29.19 Physical Applications

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

6: About MathML

… ►A good resource for finding and installing math fonts is at Fonts for MathML.

7: Guide to Searching the DLMF

… ►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. …

8: 20.14 Methods of Computation

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

9: 24.19 Methods of Computation

… ►For number-theoretic applications it is important to compute $B_{2n}(modp)$ for $2n\le p-3$; in particular to find the irregular pairs $(2n,p)$ for which $B_{2n}\equiv 0(modp)$. …

10: 7.17 Inverse Error Functions

… ►The inverses of the functions $x=\mathrm{erf}y$, $x=\mathrm{erfc}y$, $y\in ℝ$, are denoted by … ►With $t=\frac{1}{2}\sqrt{\pi }x$, …where $a_0=1$ and the other coefficients follow from the recursion … ►

$a_2=\frac{1}{8}v,$

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$a_3=-\frac{1}{32}(v^2+6v-6),$

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