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1: 24.1 Special Notation

… ►

Bernoulli Numbers and Polynomials

►The origin of the notation

B_{n}

B_{n}\left(x\right)

, is not clear. … ►

Euler Numbers and Polynomials

… ►Its coefficients were first studied in Euler (1755); they were called Euler numbers by Raabe in 1851. The notations

E_{n}

E_{n}\left(x\right)

, as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …

… ►was Professor of Mathematics at the American University of Sharjah, Sharjah, United Arab Emirates, in 1997–2005. … ►Walker’s published work has been mainly in real and complex analysis, with excursions into analytic number theory and geometry, the latter in collaboration with Professor Mowaffaq Hajja of the University of Jordan. …

3: 20 Theta Functions

…

4: 22 Jacobian Elliptic Functions

…

5: 23 Weierstrass Elliptic and Modular
Functions

…

6: Guide to Searching the DLMF

… ►

term:

a textual word, a number, or a math symbol.

►

phrase:

any double-quoted sequence of textual words and numbers.

… ►

proximity operator:

adj, prec/n, and near/n, where n is any positive natural number.

… ► ►►►

`$`	stands for any number of alphanumeric characters
	(the more conventional `*` is reserved for the multiplication operator)
…

…

7: 1.2 Elementary Algebra

… ►The arithmetic mean of

n

numbers

a_{1},a_{2},\dots,a_{n}

is … ►The geometric mean

G

and harmonic mean

H

n

positive numbers

a_{1},a_{2},\dots,a_{n}

are given by … ►If

r

is a nonzero real number, then the weighted mean

M(r)

n

nonnegative numbers

a_{1},a_{2},\dots,a_{n}

, and

n

positive numbers

p_{1},p_{2},\dots,p_{n}

with … ►The dot product notation

\mathbf{u}\cdot\mathbf{v}

is reserved for the physical three-dimensional vectors of (1.6.2). … ►The diagonal elements are not necessarily distinct, and the number of identical (degenerate) diagonal elements is the multiplicity of that specific eigenvalue. …

8: 26.11 Integer Partitions: Compositions

… ►

c\left(n\right)

denotes the number of compositions of

n

, and

c_{m}\left(n\right)

is the number of compositions into exactly

m

parts.

c\left(\in\!T,n\right)

is the number of compositions of

n

with no 1’s, where again

T=\{2,3,4,\ldots\}

. … ►

26.11.1

c\left(0\right)=c\left(\in\!T,0\right)=1.

ⓘ

Symbols:: $\in$ : element of, $c\left(\NVar{n}\right)$ : number of compositions of $n$ , $c\left(\NVar{\mathrm{condition}},\NVar{n}\right)$ : restricted number of compositions of $n$ and $T$ : set
Permalink:: http://dlmf.nist.gov/26.11.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §26.11 and Ch.26

… ►The Fibonacci numbers are determined recursively by … ►Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).

9: 27.18 Methods of Computation: Primes

§27.18 Methods of Computation: Primes

►An overview of methods for precise counting of the number of primes not exceeding an arbitrary integer

x

is given in Crandall and Pomerance (2005, §3.7). …An analytic approach using a contour integral of the Riemann zeta function (§25.2(i)) is discussed in Borwein et al. (2000). … ►These algorithms are used for testing primality of Mersenne numbers,

2^{n}-1

, and Fermat numbers,

2^{2^{n}}+1

. …

10: 26.6 Other Lattice Path Numbers

§26.6 Other Lattice Path Numbers

… ►

Delannoy Number $D(m,n)$

… ►

Motzkin Number $M(n)$

… ►

Narayana Number $N(n,k)$

… ►

§26.6(iv) Identities

…