test functions

SearchAdvancedHelp

(0.003 seconds)

1—10 of 26 matching pages

1: 1.16 Distributions

… ►

§1.16(i) Test Functions

… ► ►The linear space of all test functions with the above definition of convergence is called a test function space. … … ►Tempered distributions are continuous linear functionals on this space of test functions. …

2: 1.1 Special Notation

… ► ►►►►

$x,y$	real variables.
…
$\varphi$	a testing function.
$⟨\mathrm{\Lambda },\varphi ⟩$	action of distribution $\mathrm{\Lambda }$ on test function $\varphi$.
…

…

3: 2.6 Distributional Methods

… ►

2.6.11 $$⟨f,\varphi ⟩={\int }_0^{\mathrm{\infty }}f(t)\varphi (t)dt,$$ $\varphi \in 𝒯$.

ⓘ

Symbols:

$dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $\int$: integral, $f(t)$: locally integrable function and $𝒯$: space of decreasing functions

Referenced by:

§2.6(ii)

Permalink:

http://dlmf.nist.gov/2.6.E11

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

… ►

2.6.12 $$⟨t^{-\alpha },\varphi ⟩={\int }_0^{\mathrm{\infty }}{t}^{-\alpha }\varphi (t)dt,$$ $\varphi \in 𝒯$,

ⓘ

Symbols:

$dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $\int$: integral and $𝒯$: space of decreasing functions

Referenced by:

§2.6(iii), §2.6(iii)

Permalink:

http://dlmf.nist.gov/2.6.E12

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

… ►

2.6.13 $$⟨t^{-s-\alpha },\varphi ⟩=\frac{1}{{\left(\alpha \right)}_s}{\int }_0^{\mathrm{\infty }}{t}^{-\alpha }{\varphi }^{(s)}(t)dt,$$ $\varphi \in 𝒯$,

ⓘ

Symbols:

${\left(a\right)}_n$: Pochhammer’s symbol (or shifted factorial), $dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $\int$: integral and $𝒯$: space of decreasing functions

Referenced by:

§2.6(ii), §2.6(iii)

Permalink:

http://dlmf.nist.gov/2.6.E13

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

… ►

2.6.14 $$⟨t^{-s-1},\varphi ⟩=-\frac{1}{s!}{\int }_0^{\mathrm{\infty }}(\ln t){\varphi }^{(s+1)}(t)dt,$$ $\varphi \in 𝒯$.

ⓘ

Symbols:

$dx$: differential of $x$ , $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function, $\in$: element of, $!$: factorial (as in $n!$), $\int$: integral, $\ln z$: principal branch of logarithm function and $𝒯$: space of decreasing functions

Referenced by:

§2.6(ii), §2.6(iii)

Permalink:

http://dlmf.nist.gov/2.6.E14

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

… ►

2.6.19 $$⟨{\delta }^{(s)},\varphi ⟩={(-1)}^s{\varphi }^{(s)}(0),$$ $s=0,1,2,\mathrm{\dots }$;

ⓘ

Symbols:

${\delta }_x$: Dirac delta distribution and $⟨\mathrm{\Lambda },\varphi ⟩$: action of distribution on test function

Permalink:

http://dlmf.nist.gov/2.6.E19

Encodings:

pMML, png, TeX

See also:

Annotations for §2.6(ii), §2.6 and Ch.2

…

4: 4.48 Software

… ►Links to research literature for the Lambert $W$-function and for test software are included also. …

5: 23.20 Mathematical Applications

… ►

§23.20(iii) Factorization

…

6: 35.9 Applications

… ►For other statistical applications of ${}_p{}^{}F_q^{}$ functions of matrix argument see Perlman and Olkin (1980), Groeneboom and Truax (2000), Bhaumik and Sarkar (2002), Richards (2004) (monotonicity of power functions of multivariate statistical test criteria), Bingham et al. (1992) (Procrustes analysis), and Phillips (1986) (exact distributions of statistical test criteria). …

7: Software Index

… ►

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

…

8: Bibliography G

… ►

A monotonicity property of the power function of multivariate tests. Indag. Math. (N.S.) 11 (2), pp. 209–218.

ⓘ

External Links:

ISSN 0019-3577, Document, MathReview (Sumitra Purkayastha), ZentralBlatt

Referenced by:

§35.9.

Encodings:

BibTeX

…

9: Daniel W. Lozier

… ►His research interests have centered on numerical analysis, special functions, computer arithmetic, and mathematical software construction and testing. …

10: Bibliography C

… ►

Algorithm 714: CELEFUNT – A portable test package for complex elementary functions. ACM Trans. Math. Software 19 (1), pp. 1–21.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 714; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

►

Algorithm 715: SPECFUN – A portable FORTRAN package of special function routines and test drivers. ACM Trans. Math. Software 19 (1), pp. 22–32.

ⓘ

Notes:

Double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark. GAMS (module 715; package TOMS), ZentralBlatt

Referenced by:

3rd item, 6th item, 4th item, 2nd item, 2nd item, 2nd item, 2nd item.

Encodings:

BibTeX

…