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11: Peter Paule

… ►Paule’s main research interests are computer algebra and algorithmic mathematics, together with connections to combinatorics, special functions, number theory, and other related fields. … ►During this time he served as Associate Editor with responsibilities for all aspects of the project. …

12: 19.38 Approximations

… ►Approximations for Legendre’s complete or incomplete integrals of all three kinds, derived by Padé approximation of the square root in the integrand, are given in Luke (1968, 1970). …The accuracy is controlled by the number of terms retained in the approximation; for real variables the number of significant figures appears to be roughly twice the number of terms retained, perhaps even for $\varphi$ near $\pi /2$ with the improvements made in the 1970 reference. …

13: Guide to Searching the DLMF

… ►All terms are taken to be case-insensitive, except those taken to represent math expressions (see Case Sensitivity). … ►You can use in math queries all the symbols and commands defined in LaTeX (you can omit the $\backslash$), and some additional convenient ones, as well as the special functions’ names: … ►

All the Greek Letters (gamma vs. Gamma, sigma vs. Sigma, etc.)

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All the inverse trigonometric functions (arcsin vs. Arcsin, etc.).

… ►The natural thing is to enter the query trigonometric, and expect to have all the right matches. …

14: 27.13 Functions

… ►Goldbach’s assertion is that $S(n)\ge 1$ for all even $n>4$. … ►has nonnegative integer solutions for all $n\ge 1$. …Similarly, $G\left(k\right)$ denotes the smallest $m$ for which (27.13.1) has nonnegative integer solutions for all sufficiently large $n$. … ►for all $k\ge 2$, with equality if $4\le k\le 200,000$. … ►Exact formulas for $r_k\left(n\right)$ have also been found for $k=3,5$, and $7$, and for all even $k\le 24$. …

15: 27.1 Special Notation

§27.1 Special Notation

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$d,k,m,n$	positive integers (unless otherwise indicated).
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$p,p_1,p_2,\mathrm{\dots }$	prime numbers (or primes): integers ($>1$) with only two positive integer divisors, $1$ and the number itself.
${\sum }_p$, ${\prod }_p$	sum, product extended over all primes.
$x,y$	real numbers.
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16: Morris Newman

… ►He served as Associate Editor for Combinatorics and Number Theory for the DLMF project. … ►During this time he served as Associate Editor with responsibilities for all aspects of the project. …

17: 1.7 Inequalities

… ►Equality holds iff $a_j=c{b}_j$, $\forall j$; $c=\text{ constant}$. … ►Equality holds iff $a_j=c{b}_j$, $\forall j$; $c=\text{ constant}$. … ►Equality holds iff $Af(x)=Bg(x)$ for all $x$. … ►Equality holds iff for all $x$. … ►Equality holds iff $Af(x)=Bg(x)$ for all $x$. …

18: 32 Painlevé Transcendents

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19: 1.1 Special Notation

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$x,y$	real variables.
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$L^2(X,d\alpha )$	the space of all Lebesgue–Stieltjes measurable functions on $X$ which are square integrable with respect to $d\alpha$.
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${𝐄}_n$	the space of all $n$-dimensional vectors.
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►In the physics, applied maths, and engineering literature a common alternative to $\overline{a}$ is $a^{\ast }$, $a$ being a complex number or a matrix; the Hermitian conjugate of $𝐀$ is usually being denoted ${𝐀}^{†}$.

20: 34.14 Tables

… ►Tables of exact values of the squares of the $\mathit{3}j$ and $\mathit{6}j$ symbols in which all parameters are $\le 8$ are given in Rotenberg et al. (1959), together with a bibliography of earlier tables of $\mathit{3}j,\mathit{6}j$, and $\mathit{9}j$ symbols on pp. … ►Tables of $\mathit{3}j$ and $\mathit{6}j$ symbols in which all parameters are $\le 17/2$ are given in Appel (1968) to 6D. … ►In Varshalovich et al. (1988) algebraic expressions for the Clebsch–Gordan coefficients with all parameters $\le 5$ and numerical values for all parameters $\le 3$ are given on pp. …