De Moivre theorem

SearchAdvancedHelp

(0.001 seconds)

31—40 of 186 matching pages

31: 18 Orthogonal Polynomials

… …

32: 26.20 Physical Applications

… ►Other articles on this subject are de Bruijn (1981) and Rouvray (1995). …

33: Bibliography J

… ►

Fonctions de Mathieu et polynômes de Klein-Gordon. C. R. Acad. Sci. Paris Sér. I Math. 325 (7), pp. 713–716 (French).

ⓘ

Notes:

Translated title: Mathieu functions and Klein-Gordon polynomials.

External Links:

ISSN 0764-4442, Document, MathReview, ZentralBlatt

Referenced by:

7th item.

Encodings:

BibTeX

►

Fonctions de Mathieu et fonctions propres de l’oscillateur relativiste. Ann. Fac. Sci. Toulouse Math. (6) 7 (3), pp. 465–495 (French).

ⓘ

Notes:

Translated title: Mathieu functions and eigenfunctions of the relativistic oscillator.

External Links:

ISSN 0240-2963, Pdf, MathReview (Jean-Michel Ghez), ZentralBlatt

Referenced by:

7th item.

Encodings:

BibTeX

… ►

Sur l’inversion de $y^{\alpha }{e}^y$ au moyen des nombres de Stirling associés. C. R. Acad. Sci. Paris Sér. I Math. 320 (12), pp. 1449–1452.

ⓘ

External Links:

ISSN 0764-4442, MathReview (F. Beukers), ZentralBlatt

Referenced by:

(4.13.10).

Encodings:

BibTeX

… ►

Memoire sur l’itération des fonctions rationnelles. J. Math. Pures Appl. 8 (1), pp. 47–245 (French).

ⓘ

External Links:

FullText, ZentralBlatt

Referenced by:

§3.8(viii).

Encodings:

BibTeX

34: Wadim Zudilin

… ►de B. …

35: 30.10 Series and Integrals

… ►For an addition theorem, see Meixner and Schäfke (1954, p. 300) and King and Van Buren (1973). …

36: 10.44 Sums

… ►

§10.44(i) Multiplication Theorem

… ►

§10.44(ii) Addition Theorems

►

Neumann’s Addition Theorem

… ►

Graf’s and Gegenbauer’s Addition Theorems

…

37: 30.12 Generalized and Coulomb Spheroidal Functions

… ►

30.12.1 $$\frac{d}{dz}\left((1-z^2)\frac{dw}{dz}\right)+\left(\lambda +\alpha z+{\gamma }^2(1-z^2)-\frac{{\mu }^2}{1-z^2}\right)w=0,$$

ⓘ

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $z$: complex variable, $w$: solution to DE, $\lambda$: real parameter, ${\gamma }^2$: real parameter and $\mu$: real parameter

Referenced by:

§30.12

Permalink:

http://dlmf.nist.gov/30.12.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §30.12 and Ch.30

… ►

30.12.2 $$\frac{d}{dz}\left((1-z^2)\frac{dw}{dz}\right)+\left(\lambda +{\gamma }^2(1-z^2)-\frac{\alpha (\alpha +1)}{z^2}-\frac{{\mu }^2}{1-z^2}\right)w=0,$$

ⓘ

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $z$: complex variable, $w$: solution to DE, $\lambda$: real parameter, ${\gamma }^2$: real parameter and $\mu$: real parameter

Permalink:

http://dlmf.nist.gov/30.12.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §30.12 and Ch.30

…

38: Bibliography M

… ►

Zur Theorie des zylindrisch-parabolischen Spiegels. Z. Physik 118, pp. 343–356 (German).

ⓘ

External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§12.17.

Encodings:

BibTeX

… ►

Die Laméschen Wellenfunktionen des Drehellipsoids. Forschungsbericht No. 1952 ZWB (German).

ⓘ

Notes:

English translation: Lamé wave functions of the ellipsoid of revolution appeared as NACA Technical Memorandum No. 1224, 1949

External Links:

MathReview

Referenced by:

§30.9(iii).

Encodings:

BibTeX

… ►

A $q$-analog of the ${}_5{}^{}F_4^{}(1)$ summation theorem for hypergeometric series well-poised in $\mathrm{𝑆𝑈}(n)$ . Adv. in Math. 57 (1), pp. 14–33.

ⓘ

External Links:

ISSN 0001-8708, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§17.15.

Encodings:

BibTeX

… ►

A $q$-analog of the Gauss summation theorem for hypergeometric series in $U(n)$ . Adv. in Math. 72 (1), pp. 59–131.

ⓘ

External Links:

ISSN 0001-8708, Document, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.15.

Encodings:

BibTeX

… ►

Balanced ${}_3{}^{}\Theta _2^{}$ summation theorems for $U(n)$ basic hypergeometric series. Adv. Math. 131 (1), pp. 93–187.

ⓘ

External Links:

ISSN 0001-8708, Document, MathReview (Jiang Zeng), ZentralBlatt

Referenced by:

§17.15.

Encodings:

BibTeX

…

39: 30.2 Differential Equations

… ►

30.2.1 $$\frac{d}{dz}\left((1-z^2)\frac{dw}{dz}\right)+\left(\lambda +{\gamma }^2(1-z^2)-\frac{{\mu }^2}{1-z^2}\right)w=0.$$

ⓘ

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $z$: complex variable, $w$: solution to DE, $\lambda$: real parameter, ${\gamma }^2$: real parameter and $\mu$: real parameter

Referenced by:

§30.11(i), §30.12, §30.12, §30.13(iv), §30.14(iv), §30.16(ii), §30.2(ii), §30.2(iii), §30.3(i), §30.4(i), §30.5, §30.6, §30.6

Permalink:

http://dlmf.nist.gov/30.2.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §30.2(i), §30.2 and Ch.30

… ►

30.2.4 $$({\zeta }^2-{\gamma }^2)\frac{d^{2}w}{{d\zeta }^2}+2\zeta \frac{dw}{d\zeta }+\left({\zeta }^2-\lambda -{\gamma }^2-\frac{{\gamma }^2{\mu }^2}{{\zeta }^2-{\gamma }^2}\right)w=0.$$

ⓘ

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $w$: solution to DE, $\lambda$: real parameter, ${\gamma }^2$: real parameter, $\mu$: real parameter and $\zeta$: parameter

Referenced by:

§30.2(iii)

Permalink:

http://dlmf.nist.gov/30.2.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §30.2(ii), §30.2 and Ch.30

…

40: Diego Dominici

… ► 2023) studied Pure Mathematics at the Universidad de Buenos Aires, Argentina, and did his Ph. …