hexadecimal number system

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11: Guide to Searching the DLMF

… ►

term:

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

… ►If a query does not return any hits, the DLMF search system relaxes the query to match and retrieve what may be intended by the original query. …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 recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form. … ►The syntax of the special functions can be LaTeX-like or as employed in widely used computer algebra systems. …

12: 21.10 Methods of Computation

… ►

•

Belokolos et al. (1994, Chapter 5) and references therein. Here the Riemann surface is represented by the action of a Schottky group on a region of the complex plane. The same representation is used in Gianni et al. (1998).

►

•

Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.

…

13: Bibliography M

… ►

I. G. Macdonald (1972) Affine root systems and Dedekind’s

\eta

-function. Invent. Math. 15 (2), pp. 91–143.

ⓘ

External Links:: Document, MathReview (D.-N. Verma), ZentralBlatt
Referenced by:: §20.12(i).
Encodings:: BibTeX

►

I. G. Macdonald (1982) Some conjectures for root systems. SIAM J. Math. Anal. 13 (6), pp. 988–1007.

ⓘ

External Links:: ISSN 0036-1410, Document, MathReview (S. Milne), ZentralBlatt
Referenced by:: §17.13, §17.14.
Encodings:: BibTeX

… ►

I. G. Macdonald (2000) Orthogonal polynomials associated with root systems. Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).

ⓘ

External Links:: ISSN 1286-4889, FullText, MathReview, ZentralBlatt
Referenced by:: §18.37(iii).
Encodings:: BibTeX

… ►

Maxima (free interactive system)

ⓘ

Notes:: System for the manipulation of symbolic and numerical expressions. Includes a collection of special functions. Utilizes exact fractions, arbitrary precision integers, and arbitrary precision floating point numbers.
External Links:: Home Page
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

MuPAD (commercial interactive system and Matlab toolbox) SciFace Software, Paderborn, Germany.

ⓘ

Notes:: Computer algebra system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy
Referenced by:: § ‣ Software Cross Index.
Encodings:: BibTeX

…

14: Stephen M. Watt

… ►His areas of research include algorithms and systems for computer algebra, programming languages and compilers, mathematical handwriting recognition and mathematical document analysis. He was one of the original authors of the Maple and Axiom computer algebra systems, principal architect of the Aldor programming language and its compiler at IBM Research, and co-author of the MathML and InkML W3C standards. …

15: 28.27 Addition Theorems

… ►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. …

16: Bibliography

… ►

A. Adelberg (1996) Congruences of

p

-adic integer order Bernoulli numbers. J. Number Theory 59 (2), pp. 374–388.

ⓘ

External Links:: ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt
Referenced by:: §24.16(iii).
Encodings:: BibTeX

… ►

T. M. Apostol (2000) A Centennial History of the Prime Number Theorem. In Number Theory, Trends Math., pp. 1–14.

ⓘ

External Links:: MathReview (Giovanni Coppola), ZentralBlatt
Referenced by:: (25.16.2), (25.16.4), §25.16(i), §25.16.
Encodings:: BibTeX

… ►

J. V. Armitage (1989) The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System. In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.), London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.

ⓘ

External Links:: MathReview, ZentralBlatt
Referenced by:: §25.17.
Encodings:: BibTeX

… ►

M. Audin (1999) Spinning Tops: A Course on Integrable Systems. Cambridge Studies in Advanced Mathematics, Vol. 51, Cambridge University Press, Cambridge.

ⓘ

External Links:: ISBN 0-521-56129-9; 0-521-77919-7, MathReview (Emma Previato), ZentralBlatt
Referenced by:: §22.19(iv).
Encodings:: BibTeX

… ►

Axiom (free interactive system) Center for Algorithms and Interactive Scientific Software.

ⓘ

Notes:: Symbolic and extended-precision general purpose computer algebra system.
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

…

17: 31.15 Stieltjes Polynomials

… ►If

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

are the zeros of an

n

th degree Stieltjes polynomial

S(z)

, then every zero

z_{k}

is either one of the parameters

a_{j}

or a solution of the system of equations … ►The system (31.15.2) determines the

z_{k}

as the points of equilibrium of

n

movable (interacting) particles with unit charges in a field of

N

particles with the charges

\gamma_{j}/2

fixed at

a_{j}

. … ►

31.15.6

a_{j}<a_{j+1},

j=1,2,\dots,N-1

ⓘ

Symbols:: $j$ : nonnegative integer, $a$ : complex parameter and $N+1$ : number of singularities
Referenced by:: §31.15(iii)
Permalink:: http://dlmf.nist.gov/31.15.E6
Encodings:: pMML, png, TeX
See also:: Annotations for §31.15(ii), §31.15 and Ch.31

… ►

31.15.7

q_{j}=\gamma_{j}\sum_{k=1}^{n}\frac{1}{z_{k}-a_{j}},

j=1,2,\dots,N

ⓘ

Symbols:: $z$ : complex variable, $\gamma$ : real or complex parameter, $j$ : nonnegative integer, $n$ : nonnegative integer, $a$ : complex parameter, $q$ : real or complex parameter and $N+1$ : number of singularities
Permalink:: http://dlmf.nist.gov/31.15.E7
Encodings:: pMML, png, TeX
See also:: Annotations for §31.15(ii), §31.15 and Ch.31

… ►The normalized system of products (31.15.8) forms an orthonormal basis in the Hilbert space

L_{\rho}^{2}(Q)

. …

18: Bibliography I

… ►

IEEE (2019) IEEE International Standard for Information Technology—Microprocessor Systems—Floating-Point arithmetic: IEEE Std 754-2019. The Institute of Electrical and Electronics Engineers, Inc..

ⓘ

Notes:: IEEE Std ISO/IEC/IEEE 60559, Revision of IEEE Std 754-1985
External Links:: ISBN 978-2-88912-566-1, Document
Referenced by:: Figure 3.1.1, Figure 3.1.1, §3.1(i), §3.1(i), Erratum (V1.0.25) for Section 3.1.
Encodings:: BibTeX

… ►

K. Ireland and M. Rosen (1990) A Classical Introduction to Modern Number Theory. 2nd edition, Springer-Verlag, New York.

ⓘ

External Links:: ISBN 0-387-97329-X, MathReview (Glenn Stevens), ZentralBlatt
Referenced by:: §24.10(i), §24.10(ii), §24.10(iii), §24.17(iii).
Encodings:: BibTeX

… ►

C. Itzykson and J. Drouffe (1989) Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. Vol. 2, Cambridge University Press, Cambridge.

ⓘ

External Links:: ISBN 0-521-37012-4; 0-521-40806-7, MathReview (C. A. Hurst), ZentralBlatt
Referenced by:: 2nd item.
Encodings:: BibTeX

…

19: 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

. …

20: 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).