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1: 3.1 Arithmetics and Error Measures

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Rounding

… ►Then rounding by chopping or rounding down of $x$ gives $x_{-}$, with maximum relative error ${ϵ}_M$. …

2: 28.35 Tables

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Blanch and Rhodes (1955) includes ${\mathrm{𝐵𝑒}}_n(t)$, ${\mathrm{𝐵𝑜}}_n(t)$, $t=\frac{1}{2}\sqrt{q}$, $n=0(1)15$; 8D. The range of $t$ is 0 to 0.1, with step sizes ranging from 0.002 down to 0.00025. Notation: ${\mathrm{𝐵𝑒}}_n(t)=a_n\left(q\right)+2q-(4n+2)\sqrt{q}$, ${\mathrm{𝐵𝑜}}_n(t)=b_n\left(q\right)+2q-(4n-2)\sqrt{q}$.

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3: 26.12 Plane Partitions

… ►A plane partition, $\pi$, of a positive integer $n$, is a partition of $n$ in which the parts have been arranged in a 2-dimensional array that is weakly decreasing (nonincreasing) across rows and down columns. … ►A strict shifted plane partition is an arrangement of the parts in a partition so that each row is indented one space from the previous row and there is weak decrease across rows and strict decrease down columns. …

4: 37.13 General Orthogonal Polynomials of $d$ Variables

… ►It is often convenient to write down a basis of ${𝒱}_n^d$ in terms of multi-indices as ${\{P_{𝝂}\}}_{|𝝂|=n}$, where $𝝂\in {\mathbb{N}}_0^d$. Orderings of monomials matter in writing down an orthogonal basis. …

5: 10.40 Asymptotic Expansions for Large Argument

… ►The general terms in (10.40.6) and (10.40.7) can be written down by analogy with (10.18.17), (10.18.19), and (10.18.20). …

6: 22.19 Physical Applications

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Figure 22.19.1: Jacobi’s amplitude function $\mathrm{am}(x,k)$ for $0\le x\le 10\pi$ and $k=0.5,0.9999,1.0001,2$. …This corresponds to the pendulum being “upside down” at a point of unstable equilibrium. … Magnify

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7: 10.75 Tables

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Abramowitz and Stegun (1964, Chapter 10) tabulates $j_{\nu ,m}$, $J_{\nu }^{\prime }\left(j_{\nu ,m}\right)$, $j_{\nu ,m}^{\prime }$, $J_{\nu }\left(j_{\nu ,m}^{\prime }\right)$, $y_{\nu ,m}$, $Y_{\nu }^{\prime }\left(y_{\nu ,m}\right)$, $y_{\nu ,m}^{\prime }$, $Y_{\nu }\left(y_{\nu ,m}^{\prime }\right)$, $\nu =\frac{1}{2}(1)19⁤\frac{1}{2}$, $m=1(1)m_{\nu }$, where $m_{\nu }$ ranges from 8 at $\nu =\frac{1}{2}$ down to 1 at $\nu =19⁤\frac{1}{2}$, 6–7D.

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