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11—15 of 15 matching pages

11: 23.20 Mathematical Applications

… ►If

a,b\in\mathbb{R}

, then

C

intersects the plane

{\mathbb{R}}^{2}

in a curve that is connected if

\Delta\equiv 4a^{3}+27b^{2}>0

; if

\Delta<0

, then the intersection has two components, one of which is a closed loop. …

12: 3.6 Linear Difference Equations

… ►A “trial solution” is then computed by backward recursion, in the course of which the original components of the unwanted solution

g_{n}

die away. …

13: 33.22 Particle Scattering and Atomic and Molecular Spectra

… ►The functions

\phi_{n,\ell}(r)

defined by (33.14.14) are the hydrogenic bound states in attractive Coulomb potentials; their polynomial components are often called associated Laguerre functions; see Christy and Duck (1961) and Bethe and Salpeter (1977). …

14: 19.36 Methods of Computation

… ►

19.36.4

\begin{aligned} z_{1}&=2.10985\;99098\;8,\\ z_{3}&=2.15673\;49098\;8,\\ Z_{1}&=0.00977\;77253\;5,\end{aligned}\quad\begin{aligned} z_{2}&=2.12548\;490% 98\;8,\\ A&=2.13069\;32432\;1,\\ Z_{2}&=0.00244\;44313\;4,\end{aligned}\\ {Z_{3}=-Z_{1}-Z_{2}=-0.01222\;21566\;9,}\\ {E_{2}=\Sci{-1.25480\;14}{-4},\quad E_{3}=\Sci{-2.9212}{-7}.}

ⓘ

Symbols:: $E_{s}(\mathbf{z})$ : symmetric function, $Z_{j}$ : components and $A$
Permalink:: http://dlmf.nist.gov/19.36.E4
Encodings:: pMML, png, TeX
See also:: Annotations for §19.36(i), §19.36(i), §19.36 and Ch.19

…

15: 19.29 Reduction of General Elliptic Integrals

… ►Partial fractions provide a reduction to integrals in which

\mathbf{m}

has at most one nonzero component, and these are then reduced to basic integrals by the recurrence relations. …