completely multiplicative

SearchAdvancedHelp

(0.002 seconds)

11—16 of 16 matching pages

11: Bibliography M

… ►

Asymptotic expansion of a multiple integral. SIAM J. Math. Anal. 18 (6), pp. 1630–1637.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (E. Riekstiņš), ZentralBlatt

Referenced by:

§2.5(ii).

Encodings:

BibTeX

… ►

Algorithm 149: Complete elliptic integral. Comm. ACM 5 (12), pp. 605.

ⓘ

Notes:

Includes Algol program, maximum accuracy 10D. For remark see ACM Trans. Math. Software 4 (1978), p. 95

External Links:

ISSN 0001-0782, Document

Referenced by:

§19.39(ii).

Encodings:

BibTeX

… ►

On the evaluation of some multiple series. J. London Math. Soc. (2) 33, pp. 368–371.

ⓘ

External Links:

Document, MathReview (V. F. Cowling), ZentralBlatt

Referenced by:

(25.6.5).

Encodings:

BibTeX

… ►

Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29 (2), pp. 233–236.

ⓘ

Notes:

An Algol procedure for calculating the complete elliptic integrals of the first and the second kind with complex modulus $k$ is included.

External Links:

ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§19.36(ii), §19.39(ii).

Encodings:

BibTeX

… ►

ⓘ

Notes:

MPFR is a C library for multiple-precision floating-point computations with correct rounding. The main goal of MPFR is to provide a library for multiple-precision floating-point computation which is both efficient and has well-defined semantics. MPFR includes most of the elementary functions. It also implements the gamma function, and more special functions are planned in the future.

External Links:

MPFR

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.

Encodings:

BibTeX

…

12: 27.2 Functions

… ►

§27.2(i) Definitions

… ►They tend to thin out among the large integers, but this thinning out is not completely regular. … ►

27.2.8 $$a^{\varphi \left(n\right)}\equiv 1(modn),$$

ⓘ

Symbols:

$\varphi \left(n\right)$: Euler’s totient, $\equiv$: modular equivalence, $n$: positive integer and $a$: primitive root

A&S Ref:

24.3.2 II.B

Referenced by:

§27.16, §27.8

Permalink:

http://dlmf.nist.gov/27.2.E8

Encodings:

pMML, png, TeX

See also:

Annotations for §27.2(i), §27.2 and Ch.27

…

13: Bibliography K

… ►

On multiple zeros of derivatives of Bessel’s cylindrical functions. Dokl. Akad. Nauk SSSR 288 (2), pp. 285–288 (Russian).

ⓘ

Notes:

In Russian. English translation: Soviet Math. Dokl. 33(3), 650–653, (1986).

External Links:

ISSN 0002-3264, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(i), §10.74(vi).

Encodings:

BibTeX

►

On the calculation of the multiple complex roots of the derivatives of cylindrical Bessel functions. Zh. Vychisl. Mat. i Mat. Fiz. 27 (11), pp. 1628–1639, 1758.

ⓘ

Notes:

English translation in U.S.S.R. Computational Math. and Math. Phys. 27(6), pp. 18–25

External Links:

ISSN 0044-4669, Document, MathReview (Hans-Jürgen Albrand), ZentralBlatt

Referenced by:

§10.21(ix), §10.74(vi), 5th item.

Encodings:

BibTeX

►

Multiple complex zeros of derivatives of the cylindrical Bessel functions. Dokl. Akad. Nauk SSSR 299 (3), pp. 614–618 (Russian).

ⓘ

Notes:

In Russian. English translation: Soviet Phys. Dokl. 33(3),196–198, (1988).

External Links:

ISSN 0002-3264, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(ix), §10.74(vi).

Encodings:

BibTeX

… ►

The method of isomonodromic deformations and the asymptotics of the solutions of the “complete” third Painlevé equation. Mat. Sb. (N.S.) 134(176) (3), pp. 421–444, 448 (Russian).

ⓘ

Notes:

In Russian. English translation: Math. USSR-Sb. 62(1989), no. 2, pp. 421–444.

External Links:

ISSN 0368-8666, RussianText, Document, MathReview (J. Chrastina), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX

… ►

Some completely monotonic functions of positive order. Math. Comp. 79 (271), pp. 1697–1707.

ⓘ

External Links:

ISSN 0025-5718, Document, FullText, MathReview (Necdet Batir), ZentralBlatt

Referenced by:

§5.6(i), §5.6(i).

Encodings:

BibTeX

…

14: 18.36 Miscellaneous Polynomials

… ►These are OP’s on the interval $(-1,1)$ with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at $-1$ and $1$ to the weight function for the Jacobi polynomials. … ►

§18.36(iii) Multiple Orthogonal Polynomials

… ►This infinite set of polynomials of order $n\ge k$, the smallest power of $x$ being $x^k$ in each polynomial, is a complete orthogonal set with respect to this measure. … ►Completeness follows from the self-adjointness of $T_k$, Everitt (2008). … ►Completeness and orthogonality follow from the self-adjointness of the corresponding Schrödinger operator, Gómez-Ullate and Milson (2014), Marquette and Quesne (2013).

15: 3.11 Approximation Techniques

… ►requires approximately $n^2$ multiplications. … ►For many applications a spline function is a more adaptable approximating tool than the Lagrange interpolation polynomial involving a comparable number of parameters; see §3.3(i), where a single polynomial is used for interpolating $f(x)$ on the complete interval $[a,b]$. … ►A complete spline results by composing several Bézier curves. …

16: Bibliography

… ►

Monotonicity theorems and inequalities for the complete elliptic integrals. J. Comput. Appl. Math. 172 (2), pp. 289–312.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Živorad Tomovski), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX

… ►

Functional inequalities for complete elliptic integrals and their ratios. SIAM J. Math. Anal. 21 (2), pp. 536–549.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX

►

Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J. Math. Anal. 23 (2), pp. 512–524.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX

… ►

Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.

ⓘ

External Links:

ISSN 0030-8730, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX

…