fine structure constant

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1: 33.22 Particle Scattering and Atomic and Molecular Spectra

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$Z=m{Z}_1{Z}_2\alpha c/\mathrm{\hslash },$

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$\eta =Z_1{Z}_2\alpha c{(m/(2E))}^{1/2}.$

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$r=-Z_1{Z}_2(mc\alpha /\mathrm{\hslash })s,$

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$ϵ=E/(Z_1^2{Z}_2^{2}m{c}^2{\alpha }^2/2).$

… ► $R_{\mathrm{\infty }}=m_{\mathrm{e}}c{\alpha }^2/(2\mathrm{\hslash })$. …

2: 18.39 Applications in the Physical Sciences

… ►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. …

3: Guide to Searching the DLMF

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Table 1: Query Examples

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Query	Matching records contain
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Euler	the word ”Euler” or any of the various Euler terms such as Euler Gamma function $\mathrm{\Gamma }$, Euler Beta function $\mathrm{B}$, etc.
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Gamma near/5 =	the terms $\mathrm{\Gamma }$ and = such that $\mathrm{\Gamma }$ is up to 5 terms before or after =.
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Fine Points in Math Search

►To recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form. …