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1: 3.11 Approximation Techniques

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§3.11(v) Least Squares Approximations

… ► … ► … ► … ►For further information on least squares approximations, including examples, see Gautschi (1997a, Chapter 2) and Björck (1996, Chapters 1 and 2). …

2: Bibliography P

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On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria. Comput. J. 9 (4), pp. 404–407.

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External Links:

Document, MathReview, ZentralBlatt

Referenced by:

§3.11(ii).

Encodings:

BibTeX

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3: Bibliography B

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Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.

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External Links:

Document, ZentralBlatt

Referenced by:

§36.14(iii), §9.16.

Encodings:

BibTeX

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Uniform approximation: A new concept in wave theory. Science Progress (Oxford) 57, pp. 43–64.

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Referenced by:

§36.14(i), §9.16.

Encodings:

BibTeX

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Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

Encodings:

BibTeX

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Padé-type Approximation and General Orthogonal Polynomials. International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.

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External Links:

ISBN 3-7643-1100-2, MathReview (A. Magnus), ZentralBlatt

Referenced by:

§3.11(iv).

Encodings:

BibTeX

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Concerning an approximation of Copson. Proc. Amer. Math. Soc. 14 (4), pp. 564–568.

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External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§8.11(v), §8.11(v).

Encodings:

BibTeX

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4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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§1.18(ii) $L^2$ spaces on intervals in $ℝ$

… ►For a Lebesgue–Stieltjes measure $d\alpha$ on $X$ let $L^2(X,d\alpha )$ be the space of all Lebesgue–Stieltjes measurable complex-valued functions on $X$ which are square integrable with respect to $d\alpha$, … ►Eigenfunctions corresponding to the continuous spectrum are non-$L^2$ functions. … ►Surprisingly, if on any interval on the real line, even if positive elsewhere, as long as ${\int }_{X}q(x)dx\le 0$, see Simon (1976, Theorem 2.5), then there will be at least one eigenfunction with a negative eigenvalue, with corresponding $L^2\left(X\right)$ eigenfunction. … ►The well must be deep and broad enough to allow existence of such $L^2$ discrete states. …

5: 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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Fourier or series	at least one of the words “Fourier” or “series”.
Fourier (transform or series)	at least one of “Fourier transform” or “Fourier series”.
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J_n@(x or z)=	at least one of the math fragments $J_n(x)=$ or $J_n(z)$, emphasizing that $J_n$ is a function.
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sin x and (J_nu(z) or I_nu(z))	both $\sin x$ and at least one of the two functions $J_{\nu }(z)$ or $I_{\nu }(z)$.
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Table 3: A sample of recognized symbols

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Symbols	Comments
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~~	For approximation $\approx$.
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