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Une nouvelle représentation explicite des nombres d’Euler. C. R. Acad. Sci. Paris Sér. A-B 286 (19), pp. A807–A809.

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MathReview, ZentralBlatt

Referenced by:

§24.6.

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Rational Chebyshev approximation for the Fermi-Dirac integral $F_{-3/2}(x)$ . Solid–State Electronics 41 (5), pp. 771–773.

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Document

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§25.21(vii).

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Further comments on the computation of modified Bessel function ratios. Math. Comp. 35 (151), pp. 937–939.

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ISSN 0025-5718, FullText, Document, MathReview (James M. Horner), ZentralBlatt

Referenced by:

§10.74(v).

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Sul comportamento asintotico dell’$n$-esimo polinomio di Laguerre nell’intorno dell’ascissa $4n$ . Comment. Math. Helv. 22, pp. 150–167.

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ISSN 0010-2571, Document, MathReview (G. Szegő), ZentralBlatt

Referenced by:

§18.16(iv).

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Applied Combinatorics. 5th edition, John Wiley and Sons, New York.

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§26.15.

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3: Bibliography K

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

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1st item.

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Introduction to Solid State Physics. 7th Edition edition, John Wiley and Sons, New York.

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ISBN 0-471-11181-3

Referenced by:

§1.18(vii).

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Comment on “The incomplete beta function law for parallel tempering sampling of classical canonical systems” [J. Chem. Phys. 120, 4119 (2004)]. J. Chem. Phys. 121 (2), pp. 1167.

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Document

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§8.24(ii).

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A Program for Computing the Conical Functions of the First Kind $P_{-1/2+i\tau }^m(x)$ for $m=0$ and $m=1$ . Comput. Phys. Comm. 23 (1), pp. 51–61.

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Notes:

Single-precision Fortran, maximum accuracy 15D.

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Document, Code

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§14.31(ii), 1st item.

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Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1), pp. 177–232 (French).

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ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt

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§22.19(iv).

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4: Bibliography L

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Démonstration d’un Théoréme d’Arithmétique. Nouveau Mém. Acad. Roy. Sci. Berlin, pp. 123–133 (French).

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Notes:

Reprinted in Oeuvres, Vol. 3, pp. 189–201, Gauthier-Villars, Paris, 1867

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FullText

Referenced by:

§27.13(iii).

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Note sur la fonction $𝔎(w,x,s)={\sum }_{k=0}^{\mathrm{\infty }}\frac{e^{2k\pi ix}}{{(w+k)}^s}$ . Acta Math. 11 (1-4), pp. 19–24 (French).

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ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt

Referenced by:

§25.14(i), Notations K.

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More than one third of zeros of Riemann’s zeta-function are on $\sigma =\frac{1}{2}$ . Advances in Math. 13 (4), pp. 383–436.

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Document, MathReview (H. L. Montgomery), ZentralBlatt

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§25.10(ii), Erratum (V1.1.4) for Subsection 25.10(ii).

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Le Calcul des Résidus et ses Applications à la Théorie des Fonctions. Gauthier-Villars, Paris (French).

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Notes:

Reprinted by Éditions Jacques Gabay, Sceaux, 1989.

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ISBN 2-87647-060-8, MathReview, ZentralBlatt

Referenced by:

(25.5.10), (25.5.11), (25.5.12).

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Sur la distribution des nombres premiers. Comptes Rendus de l’Academie des Sciences, Paris 158, pp. 1869–1872 (French).

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External Links:

ZentralBlatt

Referenced by:

§27.12.

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5: Bibliography S

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On an identity of Ramanujan based on the hypergeometric series ${}_2{}^{}F_1^{}(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)$ . J. Number Theory 69 (2), pp. 125–134.

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ISSN 0022-314X, Document, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§20.11(iii).

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Répartition du courant alternatif dans un conducteur cylindrique de section elliptique. Acad. Roy. Belg. Bull. Cl. Sci. (5) 53 (8), pp. 861–878.

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6th item.

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About von Staudt congruences for Bernoulli numbers. Comment. Math. Univ. St. Paul. 48 (2), pp. 137–144.

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ISSN 0010-258X, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.10(ii).

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Some comments on Fourier analysis, uncertainty and modeling. SIAM Rev. 25 (3), pp. 379–393.

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ISSN 0036-1445, Document, MathReview (H. Vincent Poor), ZentralBlatt

Referenced by:

§30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).

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On the relative extrema of ultraspherical polynomials. Boll. Un. Mat. Ital. (3) 5, pp. 125–127.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§18.14(iii).

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6: Bibliography P

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Sur les équations différentielles du second ordre à points critiques fixès. C.R. Acad. Sc. Paris 143, pp. 1111–1117.

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ZentralBlatt

Referenced by:

§32.2(iv).

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An asymptotic representation for $\zeta (\frac{1}{2}+it)$ . Methods Appl. Anal. 4 (4), pp. 449–470.

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ISSN 1073-2772, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.9, §8.22(ii).

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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).

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Sur une généralisation des polynomes de Legendre. C. R. Acad. Sci. Paris 228, pp. 1363–1365.

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ISSN 0001-4036, MathReview (G. Szegö)

Referenced by:

§18.35(i).

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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).

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7: Bibliography D

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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.

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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction $\zeta (s)$ de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann. Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).

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Notes:

Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 223–296 Académie Royale de Belgique, Brussels, 2000.

External Links:

MathReview, ZentralBlatt

Referenced by:

§25.10(i), §27.11, §27.2(i).

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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).

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An approximation for ${\int }_{\chi }^{\mathrm{\infty }}{e}^{-t^2/2}{t}^p𝑑t,$ $\chi >0,$ $p$ real. Math. Comp. 32 (141), pp. 271–275.

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FullText, MathReview (H. E. Fettis), ZentralBlatt

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1st item.

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Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter. SIAM J. Math. Anal. 21 (4), pp. 995–1018.

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Notes:

Errata: In eq. (2.8) replace ${(x^2/4)}^2$ by ${(x^2/4)}^s$. In eq. (4.2) $\varphi (\zeta )$ should be replaced by $\psi (\zeta )$. In the second line of eq. (4.7) insert an external factor $e^{-2\pi ij/3}$ and change the upper limit of the sum to $n-1$. In eq. (4.15) the factor $\zeta$ is missing from the arguments of the functions Bi_ν and Bi’_ν.

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ISSN 0036-1410, Document, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§10.24, §10.45, §2.8(iv).

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8: 6 Exponential, Logarithmic, Sine, and
Cosine Integrals

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9: 7 Error Functions, Dawson’s and Fresnel Integrals

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