Euler splines

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1: 24.17 Mathematical Applications

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Euler Splines

… ►The functions ►

24.17.3 $$S_n(x)=\frac{{\tilde{E}}_n\left(x+\frac{1}{2}n+\frac{1}{2}\right)}{{\tilde{E}}_n\left(\frac{1}{2}n+\frac{1}{2}\right)},$$ $n=0,1,\mathrm{\dots }$,

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Symbols:

${\tilde{E}}_n\left(x\right)$: periodic Euler functions, $n$: integer and $x$: real or complex

Permalink:

http://dlmf.nist.gov/24.17.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §24.17(ii), §24.17(ii), §24.17 and Ch.24

►are called Euler splines of degree $n$. …

2: 3.11 Approximation Techniques

… ►For splines based on Bernoulli and Euler polynomials, see §24.17(ii). …

3: Bibliography C

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A note on Euler numbers and polynomials. Nagoya Math. J. 7, pp. 35–43.

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External Links:

MathReview (A. L. Whiteman), ZentralBlatt

Referenced by:

§24.10(iv).

Encodings:

BibTeX

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Calcolo delle funzioni speciali $\mathrm{\Gamma }(x)$, $\log \mathrm{\Gamma }(x)$, $\beta (x,y)$, $\mathrm{erf}(x)$, $\mathrm{erfc}(x)$ alle alte precisioni. Atti Accad. Sci. Lett. Arti Palermo Ser. (5) 2(1981/82) (1), pp. 7–25 (Italian).

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Notes:

Translated title: Computation of the special functions $\mathrm{\Gamma }(x),\log \mathrm{\Gamma }(x),\beta (x,y),\mathrm{erf}(x),\mathrm{erfc}(x)$ to a high degree of precision

External Links:

MathReview, ZentralBlatt

Referenced by:

§5.24(ii).

Encodings:

BibTeX

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$\gamma$ rays from an extranuclear direct capture process. Nuclear Physics 24 (1), pp. 89–101.

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External Links:

Document

Referenced by:

§33.22(v).

Encodings:

BibTeX

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Multivariate Splines. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 54, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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Notes:

With an appendix by Harvey Diamond

External Links:

ISBN 0-89871-226-2, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.11(vi).

Encodings:

BibTeX

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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.

Encodings:

BibTeX

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