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11: 18.39 Applications in the Physical Sciences

… ►Physical scientists use the $n$ of Bohr as, to $0$th and $1$st order, it describes the structure and organization of the Periodic Table of the Chemical Elements of which the Hydrogen atom is only the first. … ►A relativistic treatment becoming necessary as $Z$ becomes large as corrections to the non-relativistic Schrödinger picture are of approximate order ${\left(\alpha Z\right)}^2\sim {\left(Z/137\right)}^2$, $\alpha$ being the dimensionless fine structure constant $e^2/(4\pi {\epsilon }_0\mathrm{\hslash }c)$, where $c$ is the speed of light. … ►Table 18.39.1 lists typical non-classical weight functions, many related to the non-classical Freud weights of §18.32, and §32.15, all of which require numerical computation of the recursion coefficients (i. … ►with matrix eigenvalues $ϵ={ϵ}_i^N$, $i=1,2,\mathrm{\dots },N$, and the eigenvectors, $𝐜(ϵ)=(c_0(ϵ),c_1(ϵ),\mathrm{\dots },c_{N-1}(ϵ))$, are determined by the recursion relation (18.39.46) below. …

12: Bibliography

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Some series of the zeta and related functions. Analysis (Munich) 18 (2), pp. 131–144.

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External Links:

ISSN 0174-4747, MathReview (Jack Quine), ZentralBlatt

Referenced by:

(25.11.37), (25.11.38), (25.11.39), (25.11.40), §25.11, §25.11(xi), (25.8.1), (25.8.4), §25.8.

Encodings:

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Some determinants of Bernoulli, Euler and related numbers. Portugal. Math. 18, pp. 91–99.

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External Links:

FullText, MathReview (D. P. Banerjee), ZentralBlatt

Referenced by:

§24.14(ii).

Encodings:

BibTeX

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Study of nuclear structure by electromagnetic excitation with accelerated ions. Rev. Mod. Phys. 28, pp. 432–542.

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External Links:

ISSN 0034-6861, Document, MathReview, ZentralBlatt

Referenced by:

§33.22(ii).

Encodings:

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Algorithm 588. Fast Hankel transforms using related and lagged convolutions. ACM Trans. Math. Software 8 (4), pp. 369–370.

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Notes:

Single-precision Fortran, maximum accuracy 8S.

External Links:

ISSN 0098-3500, Document, GAMS (module 588; package TOMS)

Referenced by:

2nd item.

Encodings:

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Integral equations and relations for Lamé functions. Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.

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External Links:

Document, MathReview (I. Marx), ZentralBlatt

Referenced by:

§29.8.

Encodings:

BibTeX

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