von Staudt–Clausen theorem

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1: 24.10 Arithmetic Properties

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§24.10(i) Von Staudt–Clausen Theorem

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2: Bibliography C

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The Staudt-Clausen theorem. Math. Mag. 34, pp. 131–146.

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External Links:

MathReview (K. Goldberg), ZentralBlatt

Referenced by:

§24.6.

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New proof of the addition theorem for Gegenbauer polynomials. SIAM J. Math. Anal. 2, pp. 347–351.

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ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§18.18(ii).

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Short proofs of three theorems on elliptic integrals. SIAM J. Math. Anal. 9 (3), pp. 524–528.

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External Links:

Document, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§19.26(i).

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The universal von Staudt theorems. Trans. Amer. Math. Soc. 315 (2), pp. 591–603.

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ISSN 0002-9947, FullText, MathReview (T. Metsänkylä), ZentralBlatt

Referenced by:

§24.16(iii).

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Über die Fälle, wenn die Reihe von der Form $y=1+\frac{\alpha }{1}\cdot \frac{\beta }{\gamma }x+\frac{\alpha \cdot \alpha +1}{1\cdot 2}\cdot \frac{\beta \cdot \beta +1}{\gamma \cdot \gamma +1}{x}^2+$ etc. ein Quadrat von der Form $z=1+\frac{{\alpha }^{\prime }}{1}\cdot \frac{{\beta }^{\prime }}{{\gamma }^{\prime }}\cdot \frac{{\delta }^{\prime }}{{ϵ}^{\prime }}x+\frac{{\alpha }^{\prime }\cdot {\alpha }^{\prime }+1}{1\cdot 2}\cdot \frac{{\beta }^{\prime }\cdot {\beta }^{\prime }+1}{{\gamma }^{\prime }\cdot {\gamma }^{\prime }+1}\cdot \frac{{\delta }^{\prime }\cdot {\delta }^{\prime }+1}{{ϵ}^{\prime }\cdot {ϵ}^{\prime }+1}{x}^2+$ etc. hat. J. Reine Angew. Math. 3, pp. 89–91.

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External Links:

Link, MathReview Entry, ZentralBlatt

Referenced by:

§16.12.

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3: Bibliography K

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The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers. Math. Ann. 216 (1), pp. 1–4.

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ISSN 0025-5831, Document, MathReview (M. Basmakov), ZentralBlatt

Referenced by:

§24.16(iii).

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Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution. Justus von Liebig Verlag, Darmstadt (German, English).

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Notes:

In cooperation with W. Rudert

External Links:

MathReview, ZentralBlatt

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1st item.

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An extension of Saalschütz’s summation theorem for the series ${}_{r+3}{}^{}F_{r+2}^{}$ . Integral Transforms Spec. Funct. 24 (11), pp. 916–921.

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ISSN 1065-2469, Document, FullText, MathReview (Christian Lavault), ZentralBlatt

Referenced by:

§16.4(ii), §16.4(ii).

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A general addition theorem for spheroidal wave functions. SIAM J. Math. Anal. 4 (1), pp. 149–160.

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External Links:

Document, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§30.10.

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A new proof of a Paley-Wiener type theorem for the Jacobi transform. Ark. Mat. 13, pp. 145–159.

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External Links:

Document, MathReview (G. Gasper), ZentralBlatt

Referenced by:

§18.10(i).

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4: Bibliography G

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Die Beugung einer ebenen elektromanetischen Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt. Ann. Physik (7) 468, pp. 237–251 (German).

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External Links:

Document, ZentralBlatt

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6th item.

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A theorem on the numerators of the Bernoulli numbers. Amer. Math. Monthly 97 (2), pp. 136–138.

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ISSN 0002-9890, FullText, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.10(iv), §24.16(iii).

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Von Staudt for ${𝐅}_q[T]$ . Duke Math. J. 45 (4), pp. 885–910.

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ISSN 0012-7094, Document, MathReview (Neal Koblitz), ZentralBlatt

Referenced by:

§24.16(iii).

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Multilateral summation theorems for ordinary and basic hypergeometric series in $\mathrm{U}(n)$ . SIAM J. Math. Anal. 18 (6), pp. 1576–1596.

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ISSN 0036-1410, Document, MathReview, ZentralBlatt

Referenced by:

§17.15.

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5: Bibliography S

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Über einige Integrale mit Produkten von Mathieu-Funktionen. Arch. Math. (Basel) 41 (2), pp. 152–162.

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ISSN 0003-889X, Document, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§28.28(iii), §28.28(iv).

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Sturm oscillation and comparison theorems. In Sturm-Liouville theory, pp. 29–43.

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External Links:

Document, Link, MathReview Entry

Referenced by:

§18.36(vi), §18.39(i).

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Szegő’s Theorem and Its Descendants. Spectral Theory for $L^2$ Perturbations of Orthogonal Polynomials. M. B. Porter Lectures, Princeton University Press, Princeton, NJ.

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External Links:

ISBN 978-0-691-14704-8, MathReview (Harry Dym)

Referenced by:

§18.2(xi).

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Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.

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External Links:

ISSN 0285-4821, MathReview (Peter M. Neumann), ZentralBlatt

Referenced by:

§24.10(ii).

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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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6: Annie A. M. Cuyt

… ►Subsequently she was a Research fellow with the Alexander von Humboldt Foundation (Germany), she obtained the Habilitation (1986) and became author or co-author of several books, including Handbook of Continued Fractions for Special Functions. …

7: Diego Dominici

… ►In 2008 Dominici received a Research Fellowship from the Alexander von Humboldt Foundation and visited the Technische Universität Berlin in Germany. …

8: 27.12 Asymptotic Formulas: Primes

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Prime Number Theorem

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9: 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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Handbuch der Lehre von der Verteilung der Primzahlen. 2 Bände. Chelsea Publishing Co., New York (German).

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Notes:

2nd edition, with an appendix by Paul T. Bateman

External Links:

MathReview (L. Schoenfeld), ZentralBlatt

Referenced by:

(25.8.2).

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Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpolynomen. Z. Angew. Math. Mech. 76 (3), pp. 181–184.

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External Links:

ISSN 0044-2267, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(18.34.5_5).

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10: 28.27 Addition Theorems

§28.27 Addition Theorems

►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. They are analogous to the addition theorems for Bessel functions (§10.23(ii)) and modified Bessel functions (§10.44(ii)). …