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11: 15.4 Special Cases

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§15.4(ii) Argument Unity

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12: 3.2 Linear Algebra

… ►In practice, if any of the multipliers ${\mathrm{\ell }}_{jk}$ are unduly large in magnitude compared with unity, then Gaussian elimination is unstable. …

13: 3.8 Nonlinear Equations

… ►For moderate or large values of $n$ it is not uncommon for the magnitude of the right-hand side of (3.8.14) to be very large compared with unity, signifying that the computation of zeros of polynomials is often an ill-posed problem. …

14: Bibliography M

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On the Representation of Meijer’s $G$-Function in the Vicinity of Singular Unity. In Complex Analysis and Applications ’81 (Varna, 1981), pp. 383–398.

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External Links:

MathReview (B. D. Agrawal), ZentralBlatt

Referenced by:

§16.21.

Encodings:

BibTeX

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15: 1.2 Elementary Algebra

… ►A vector of $l^2$ norm unity is normalized and every non-zero vector $𝐯$ can be normalized via $𝐯\to 𝐯/\Vert 𝐯\Vert$. …

16: 18.30 Associated OP’s

… ►The simplicity of the relationship follows from the fact that the monic polynomials have been rescaled so that the coefficient of the highest power of $x$ in $p_n(x)$, namely, $x^n$, is unity; for a note on this standardization, see §18.2(iii). …

17: 3.5 Quadrature

… ►The $p_n(x)$ are the monic Legendre polynomials, that is, the polynomials $P_n\left(x\right)$ (§18.3) scaled so that the coefficient of the highest power of $x$ in their explicit forms is unity. …