DLMF: Untitled Document

… … ► 1969 in Villarrobledo, Spain) is Associate Professor in the Department of Applied Mathematics and Computer Science in the Universidad de Cantabria, Spain. … ► M. …

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M. D’Ocagne (1904) Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli. Bull. Sci. Math. (2) 28, pp. 29–32 (French).

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External Links:: ZentralBlatt
Referenced by:: §24.1.
Encodings:: BibTeX

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M. G. de Bruin, E. B. Saff, and R. S. Varga (1981a) On the zeros of generalized Bessel polynomials. I. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 1–13.

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External Links:: ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt
Referenced by:: §10.49(ii), §10.58.
Encodings:: BibTeX

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M. G. de Bruin, E. B. Saff, and R. S. Varga (1981b) On the zeros of generalized Bessel polynomials. II. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 14–25.

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External Links:: ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt
Referenced by:: §10.49(ii), §10.58.
Encodings:: BibTeX

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C. de la Vallée Poussin (1896b) Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire

Mx+N

. Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).

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Notes:: Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 309–425, Académie Royale de Belgique, Brussels, 2000.
External Links:: MathReview, ZentralBlatt
Referenced by:: §25.10(i), §27.11, §27.2(i).
Encodings:: BibTeX

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A. Decarreau, M.-Cl. Dumont-Lepage, P. Maroni, A. Robert, and A. Ronveaux (1978a) Formes canoniques des équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.

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External Links:: MathReview (A. E. Danese), ZentralBlatt
Referenced by:: §31.12.
Encodings:: BibTeX

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… … ►M. …

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L. Jager (1997) Fonctions de Mathieu et polynômes de Klein-Gordon. C. R. Acad. Sci. Paris Sér. I Math. 325 (7), pp. 713–716 (French).

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Notes:: Translated title: Mathieu functions and Klein-Gordon polynomials.
External Links:: ISSN 0764-4442, Document, MathReview, ZentralBlatt
Referenced by:: 7th item.
Encodings:: BibTeX

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L. Jager (1998) Fonctions de Mathieu et fonctions propres de l’oscillateur relativiste. Ann. Fac. Sci. Toulouse Math. (6) 7 (3), pp. 465–495 (French).

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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

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D. J. Jeffrey, R. M. Corless, D. E. G. Hare, and D. E. Knuth (1995) 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.

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External Links:: ISSN 0764-4442, MathReview (F. Beukers), ZentralBlatt
Referenced by:: (4.13.10).
Encodings:: BibTeX

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M. Jimbo, T. Miwa, Y. Môri, and M. Sato (1980) Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1 (1), pp. 80–158.

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External Links:: ISSN 0167-2789, Document, MathReview, ZentralBlatt
Referenced by:: §32.16.
Encodings:: BibTeX

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G. Julia (1918) Memoire sur l’itération des fonctions rationnelles. J. Math. Pures Appl. 8 (1), pp. 47–245 (French).

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External Links:: FullText, ZentralBlatt
Referenced by:: §3.8(viii).
Encodings:: BibTeX

… ►For

n\geq 0

the

m

th positive zeros of

\mathsf{j}_{n}\left(x\right)

,

\mathsf{j}_{n}'\left(x\right)

,

\mathsf{y}_{n}\left(x\right)

, and

\mathsf{y}_{n}'\left(x\right)

are denoted by

a_{n,m}

,

a^{\prime}_{n,m}

,

b_{n,m}

, and

b^{\prime}_{n,m}

, respectively, except that for

n=0

we count

x=0

as the first zero of

\mathsf{j}_{0}'\left(x\right)

. … ►

a_{n,m}=j_{n+\frac{1}{2},m},

… ►Hence properties of

a_{n,m}

and

b_{n,m}

are derivable straightforwardly from results given in §§10.21(i)–10.21(iii), 10.21(vi)–10.21(viii), and 10.21(x). …For some properties of

a^{\prime}_{n,m}

and

b^{\prime}_{n,m}

, including asymptotic expansions, see Olver (1960, pp. xix–xxi). ►See also Davies (1973), de Bruin et al. (1981a, b), and Gottlieb (1985).

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G. Petiau (1955) La Théorie des Fonctions de Bessel Exposée en vue de ses Applications à la Physique Mathématique. Centre National de la Recherche Scientifique, Paris (French).

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External Links:: MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: §10.63(ii).
Encodings:: BibTeX

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F. Pollaczek (1949a) Sur une généralisation des polynomes de Legendre. C. R. Acad. Sci. Paris 228, pp. 1363–1365.

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External Links:: ISSN 0001-4036, MathReview (G. Szegö)
Referenced by:: §18.35(i).
Encodings:: BibTeX

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F. Pollaczek (1949b) Systèmes de polynomes biorthogonaux qui généralisent les polynomes ultrasphériques. C. R. Acad. Sci. Paris 228, pp. 1998–2000.

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External Links:: ISSN 0001-4036, MathReview (G. Szegö)
Referenced by:: §18.35(i).
Encodings:: BibTeX

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F. Pollaczek (1950) Sur une famille de polynômes orthogonaux à quatre paramètres. C. R. Acad. Sci. Paris 230, pp. 2254–2256.

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External Links:: MathReview (A. Erdélyi)
Referenced by:: (18.30.17), (18.30.18), (18.35.6_5), (18.35.6_6), §18.35(i).
Encodings:: BibTeX

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G. P. M. Poppe and C. M. J. Wijers (1990) Algorithm 680: Evaluation of the complex error function. ACM Trans. Math. Software 16 (1), pp. 47.

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Notes:: Single-precision Fortran, maximum accuracy 14S.
External Links:: ISSN 0098-3500, Document, GAMS (module 680; package TOMS), MathReview, ZentralBlatt
Referenced by:: 1st item.
Encodings:: BibTeX

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34.6.1

\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}=\sum_{\mbox{\scriptsize all }m_{rs}}\begin{% pmatrix}j_{11}&j_{12}&j_{13}\\ m_{11}&m_{12}&m_{13}\end{pmatrix}\begin{pmatrix}j_{21}&j_{22}&j_{23}\\ m_{21}&m_{22}&m_{23}\end{pmatrix}\begin{pmatrix}j_{31}&j_{32}&j_{33}\\ m_{31}&m_{32}&m_{33}\end{pmatrix}\*\begin{pmatrix}j_{11}&j_{21}&j_{31}\\ m_{11}&m_{21}&m_{31}\end{pmatrix}\begin{pmatrix}j_{12}&j_{22}&j_{32}\\ m_{12}&m_{22}&m_{32}\end{pmatrix}\begin{pmatrix}j_{13}&j_{23}&j_{33}\\ m_{13}&m_{23}&m_{33}\end{pmatrix},

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Defines:: $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol
Symbols:: $\begin{pmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{m_{1}}&\NVar{m_{2}}&\NVar{m_{3}}\end{pmatrix}$ : $\mathit{3j}$ symbol, $j,j_{r}$ : non-negative integers or non-negative integers plus one half., $r$ : nonnegative integer and $s$ : integer
Permalink:: http://dlmf.nist.gov/34.6.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §34.6 and Ch.34

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N. Nielsen (1906b) Theorie des Integrallogarithmus und verwandter Transzendenten. B. G. Teubner, Leipzig (German).

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Notes:: For a reprint with corrections see Nielsen (1965).
External Links:: ZentralBlatt (G. Kowalewski)
Referenced by:: §6.14(i), §6.14(ii), §6.14(iii), §6.7(ii), §6.7(iv), §6.9.
Encodings:: BibTeX

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N. Nielsen (1923) Traité Élémentaire des Nombres de Bernoulli. Gauthier-Villars, Paris.

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External Links:: ZentralBlatt
Referenced by:: §24.1.
Encodings:: BibTeX

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N. Nielsen (1965) Die Gammafunktion. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten. Chelsea Publishing Co., New York (German).

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Notes:: Both books are textually unaltered except for correction of errata.
External Links:: MathReview
Referenced by:: N. Nielsen (1906a), N. Nielsen (1906b).
Encodings:: BibTeX

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M. M. Nieto and L. M. Simmons (1979) Eigenstates, coherent states, and uncertainty products for the Morse oscillator. Phys. Rev. A (3) 19 (2), pp. 438–444.

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External Links:: ISSN 1050-2947, Document, Link, MathReview Entry
Referenced by:: (18.39.17), (18.39.18).
Encodings:: BibTeX

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N. E. Nörlund (1922) Mémoire sur les polynomes de Bernoulli. Acta Math. 43, pp. 121–196 (French).

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External Links:: Document, ZentralBlatt
Referenced by:: §24.13(i), §24.13(ii), §24.14(i), Ch.24.
Encodings:: BibTeX

…

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H. C. van de Hulst (1957) Light Scattering by Small Particles. John Wiley and Sons. Inc., New York.

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External Links:: MathReview (P. M. Morse)
Referenced by:: §9.16.
Encodings:: BibTeX

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H. C. van de Hulst (1980) Multiple Light Scattering. Vol. 1, Academic Press, New York.

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Referenced by:: §6.17.
Encodings:: BibTeX

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J. van de Lune, H. J. J. te Riele, and D. T. Winter (1986) On the zeros of the Riemann zeta function in the critical strip. IV. Math. Comp. 46 (174), pp. 667–681.

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External Links:: ISSN 0025-5718, FullText, Document, MathReview (Jürgen G. Hinz), ZentralBlatt
Referenced by:: §25.10(ii), §25.18(ii).
Encodings:: BibTeX

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H. Van de Vel (1969) On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.

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External Links:: FullText, MathReview, ZentralBlatt
Referenced by:: §19.12, §19.5.
Encodings:: BibTeX

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A. N. Vavreck and W. Thompson (1984) Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.

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External Links:: ISSN 0033-569X, MathReview (A. de Castro Brzezicki), ZentralBlatt
Referenced by:: §10.60(iii), §10.60(iii).
Encodings:: BibTeX

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L. Robin (1957) Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome I. Gauthier-Villars, Paris.

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Notes:: Préface de H. Villat
External Links:: MathReview (R. Campbell), ZentralBlatt
Referenced by:: Ch.14.
Encodings:: BibTeX

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L. Robin (1958) Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome II. Gauthier-Villars, Paris.

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External Links:: MathReview (R. Campbell), ZentralBlatt
Referenced by:: Ch.14.
Encodings:: BibTeX

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L. Robin (1959) Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome III. Collection Technique et Scientifique du C. N. E. T. Gauthier-Villars, Paris.

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External Links:: MathReview (R. Campbell), ZentralBlatt
Referenced by:: Ch.14.
Encodings:: BibTeX

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V. Romanovski (1929) Sur quelques classes nouvelles de polynômes orthogonaux. C. R. Acad. Sci. Paris 188, pp. 1023–1025.

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External Links:: ZentralBlatt
Referenced by:: (18.34.5_5).
Encodings:: BibTeX

… ►

R. R. Rosales (1978) The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent. Proc. Roy. Soc. London Ser. A 361, pp. 265–275.

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External Links:: FullText, MathReview (A. D. Brjuno), ZentralBlatt
Referenced by:: §32.11(ii), §32.17, §32.3(ii).
Encodings:: BibTeX

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probl�me des m�nages

1—10 of 485 matching pages

1: Amparo Gil

2: Bibliography D

3: Javier Segura

4: Bibliography J

5: 10.58 Zeros

6: Bibliography P

7: 34.6 Definition: $\mathit{9j}$ Symbol

8: Bibliography N

9: Bibliography V

10: Bibliography R