cardinal monosplines

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1: 24.17 Mathematical Applications

… ►The functions … ►

Bernoulli Monosplines

►A function of the form $x^n-S(x)$, with $S(x)\in {𝒮}_{n-1}$ is called a cardinal monospline of degree $n$. …For each $n=1,2,\mathrm{\dots }$ the function $M_n(x)$ is also the unique cardinal monospline of degree $n$ satisfying (24.17.6), provided that … ► …

2: 26.18 Counting Techniques

… ►

26.18.1

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Symbols:

$\left|A\right|$: number of elements of a finite set $A$ , $\cap$: intersection, $\setminus$: set subtraction, $\cup$: union, $j$: nonnegative integer, $n$: nonnegative integer, $A_k$: subsets and $S$: set

Permalink:

http://dlmf.nist.gov/26.18.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §26.18 and Ch.26

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3: 26.1 Special Notation

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$x$	real variable.
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$\left|A\right|$	number of elements of a finite set $A$.
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4: 3.3 Interpolation

… ►For interpolation of a bounded function $f$ on $ℝ$ the cardinal function of $f$ is defined by ►

3.3.43 $$C(f,h)(x)=\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}f(kh)S(k,h)(x),$$

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Defines:

$C(f,h)$: cardinal function of $f$ (locally)

Symbols:

$f(z)$: function and $S(k,h)(x)$: Sinc function

Permalink:

http://dlmf.nist.gov/3.3.E43

Encodings:

pMML, png, TeX

See also:

Annotations for §3.3(vi), §3.3 and Ch.3

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5: Bibliography S

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Cardinal Spline Interpolation. Society for Industrial and Applied Mathematics, Philadelphia, PA.

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Notes:

Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12

External Links:

MathReview (H. L. Loeb), ZentralBlatt

Referenced by:

§24.17(ii).

Encodings:

BibTeX

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