psi%20function

SearchAdvancedHelp

(0.003 seconds)

11—14 of 14 matching pages

11: 36.5 Stokes Sets

… ►Stokes sets are surfaces (codimension one) in $𝐱$ space, across which ${\mathrm{\Psi }}_K(𝐱;k)$ or ${\mathrm{\Psi }}^{(\mathrm{U})}(𝐱;k)$ acquires an exponentially-small asymptotic contribution (in $k$), associated with a complex critical point of ${\mathrm{\Phi }}_K$ or . … ►

$K=1$. Airy Function

… ►

36.5.4 $$80x^5-40x^4-55x^3+5x^2+20x-1=0,$$

ⓘ

Symbols:

$x$: real parameter

Permalink:

http://dlmf.nist.gov/36.5.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §36.5(ii), §36.5(ii), §36.5 and Ch.36

… ►

36.5.7 $$X=\frac{9}{20}+20u^4-\frac{Y^2}{20u^2}+6u^2\mathrm{sign}\left(z\right),$$

ⓘ

Symbols:

$\mathrm{sign}x$: sign of, $z$: real parameter, $X$: scaled coordinate and $Y$: scaled coordinate

Permalink:

http://dlmf.nist.gov/36.5.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §36.5(ii), §36.5(ii), §36.5 and Ch.36

…

12: Software Index

… ► ►►►

	Open Source													With Book						Commercial
…
20 Theta Functions
…

►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►In the list below we identify four main sources of software for computing special functions. … ►

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.

… ►The following are web-based software repositories with significant holdings in the area of special functions. …

13: 18.39 Applications in the Physical Sciences

… ► $\mathscr{H}$ also controls time evolution of the wave function $\mathrm{\Psi }(x,t)$ via the time-dependent Schrödinger equation, … ►If $\mathrm{\Psi }(x,t=0)=\chi (x)$ is an arbitrary unit normalized function in the domain of $\mathscr{H}$ then, by self-adjointness, … ►The finite system of functions ${\psi }_n$ is orthonormal in $L^2(ℝ,dx)$, see (18.34.7_3). … ►An alternative, and often used, form of (18.39.25) is that for the spherical radial function ${\psi }_{n,l}(r)=r{R}_{n,l}(r)$, … ►The functions ${\psi }_{p,l}(r)$ satisfy the equation, …

14: Bibliography C

… ►

The hypergeometric function and the $R$-function near their branch points. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 63–89.

ⓘ

Notes:

International conference on special functions: theory and computation (Turin, 1984)

External Links:

ISSN 0373-1243, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§19.27(vi).

Encodings:

BibTeX

… ►

Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

ⓘ

External Links:

ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

Encodings:

BibTeX

… ►

Chebyshev approximations for the psi function. Math. Comp. 27 (121), pp. 123–127.

ⓘ

External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§5.23(i).

Encodings:

BibTeX

… ►

Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

ⓘ

External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

BibTeX

… ►

Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

ⓘ

External Links:

Document

Referenced by:

5th item.

Encodings:

BibTeX

…