extremal%20properties

SearchAdvancedHelp

(0.003 seconds)

1—10 of 278 matching pages

1: 30.15 Signal Analysis

… ►

§30.15(v) Extremal Properties

…

2: Bibliography D

… ►

Computational properties of three-term recurrence relations for Kummer functions. J. Comput. Appl. Math. 233 (6), pp. 1505–1510.

ⓘ

External Links:

ISSN 0377-0427, Document, FullText, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§13.29(iv), §13.29(iv).

Encodings:

BibTeX

… ►

Sharp bounds for the extreme zeros of classical orthogonal polynomials. J. Approx. Theory 162 (10), pp. 1793–1804.

ⓘ

External Links:

ISSN 0021-9045, Document, FullText, MathReview (Francisco Marcellán), ZentralBlatt

Referenced by:

(18.16.12), (18.16.13), §18.16(ii), §18.16(ii), §18.16(iv).

Encodings:

BibTeX

… ►

Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

ⓘ

Notes:

For a numerical error in one of the zeros see Amos (1985).

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

… ►

Inequalities for extreme zeros of some classical orthogonal and $q$-orthogonal polynomials. Math. Model. Nat. Phenom. 8 (1), pp. 48–59.

ⓘ

External Links:

ISSN 0973-5348, Document, FullText, MathReview (Ana Foulquié Moreno), ZentralBlatt

Referenced by:

§18.16(ii), §18.16(iv), §18.16(ii), §18.16(iv), §18.27(iv), §18.27(iv), §18.27(v), §18.27(v).

Encodings:

BibTeX

… ►

Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

ⓘ

Notes:

(This reference has several typographical errors.)

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

Encodings:

BibTeX

…

3: Bibliography I

… ►

The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

ⓘ

External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

BibTeX

… ►

Bound on the extreme zeros of orthogonal polynomials. Proc. Amer. Math. Soc. 115 (1), pp. 131–140.

ⓘ

External Links:

ISSN 0002-9939, Document, MathReview (E. R. Love), ZentralBlatt

Referenced by:

(18.16.12), (18.16.13).

Encodings:

BibTeX

…

4: 35.10 Methods of Computation

… ►These algorithms are extremely efficient, converge rapidly even for large values of $m$, and have complexity linear in $m$.

5: Bibliography C

… ►

Some reformulated properties of Jacobian elliptic functions. J. Math. Anal. Appl. 323 (1), pp. 522–529.

ⓘ

External Links:

ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§19.25(v), §19.25(v), §22.13(i), §22.13(ii), §22.13(iii), §22.14(i), §22.14(ii).

Encodings:

BibTeX

… ►

Stability properties of disk polynomials. Numer. Algorithms.

ⓘ

External Links:

Document

Referenced by:

(18.14.3_5).

Encodings:

BibTeX

… ►

Extremal measures for a system of orthogonal polynomials. Constr. Approx. 9, pp. 111–119.

ⓘ

External Links:

ISSN 0176-4276, Document, MathReview (Mizan Rahman), ZentralBlatt

Referenced by:

§18.28(iv).

Encodings:

BibTeX

… ►

Properties of generalized Freud polynomials. J. Approx. Theory 225, pp. 148–175.

ⓘ

External Links:

ISSN 0021-9045, Document, Link, MathReview (Maria das Neves Rebocho)

Referenced by:

§18.32.

Encodings:

BibTeX

… ►

Quasinormal modes of the extremal BTZ black hole. Classical Quantum Gravity 21 (12), pp. 2801–2809.

ⓘ

External Links:

ISSN 0264-9381, MathReview (Donato Bini), ZentralBlatt

Referenced by:

§13.28(iii).

Encodings:

BibTeX

…

6: William P. Reinhardt

… ►Reinhardt is a theoretical chemist and atomic physicist, who has always been interested in orthogonal polynomials and in the analyticity properties of the functions of mathematical physics. … ►

20 Theta Functions

… ►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.

7: 3.8 Nonlinear Equations

… ►

3.8.15 $$p(x)=(x-1)(x-2)\mathrm{\cdots }(x-20)$$

ⓘ

Permalink:

http://dlmf.nist.gov/3.8.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §3.8(vi), §3.8(vi), §3.8 and Ch.3

►are well separated but extremely ill-conditioned. Consider $x=20$ and $j=19$. We have $p^{\prime }(20)=19!$ and $a_{19}=1+2+\mathrm{\cdots }+20=210$. … ►

3.8.16 $$\frac{dx}{d{a}_{19}}=-\frac{{20}^{19}}{19!}=(-4.30\mathrm{\dots })\times {10}^7.$$

ⓘ

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ and $!$: factorial (as in $n!$)

Permalink:

http://dlmf.nist.gov/3.8.E16

Encodings:

pMML, png, TeX

See also:

Annotations for §3.8(vi), §3.8(vi), §3.8 and Ch.3

…

8: Mathematical Introduction

… ►In addition, there is a comprehensive account of the great variety of analytical methods that are used for deriving and applying the extremely important asymptotic properties of the special functions, including double asymptotic properties (Chapter 2 and §§10.41(iv), 10.41(v)). …

9: 20 Theta Functions

Chapter 20 Theta Functions

…

10: 25.12 Polylogarithms

… ►

§25.12(i) Dilogarithms

… ►For graphics see Figures 25.12.1 and 25.12.2, and for further properties see Maximon (2003), Kirillov (1995), Lewin (1981), Nielsen (1909), and Zagier (1989). … ►

►

►

Figure 25.12.2: Absolute value of the dilogarithm function $\left|{\mathrm{Li}}_2\left(x+\mathrm{i}y\right)\right|$, $-20\le x\le 20$, $-20\le y\le 20$. … Magnify 3D Help

►

§25.12(ii) Polylogarithms

… ►Further properties include …