sums of squares
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21: 1.2 Elementary Algebra
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§1.2(vi) Square Matrices
… ► ►Special Forms of Square Matrices
… ►Norms of Square Matrices
… ►Non-Defective Square Matrices
…22: Bibliography
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On magic squares constructed by the uniform step method.
Proc. Amer. Math. Soc. 2 (4), pp. 557–565.
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Theorems on generalized Dedekind sums.
Pacific J. Math. 2 (1), pp. 1–9.
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Bernoulli’s power-sum formulas revisited.
Math. Gaz. 90 (518), pp. 276–279.
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Positive Jacobi polynomial sums. II.
Amer. J. Math. 98 (3), pp. 709–737.
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Jacobi polynomials. I. New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum.
SIAM J. Math. Anal. 5, pp. 119–124.
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23: 3.5 Quadrature
24: 14.28 Sums
§14.28 Sums
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14.28.1
►where the branches of the square roots have their principal values when and are continuous when .
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14.28.2
, ,
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§14.28(iii) Other Sums
…25: 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). …26: Errata
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Equations (1.8.5), (1.8.6)
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1.8.5
1.8.6
Previously these equations were given as inequalities. For square integrable functions the inequality can be sharpened to .
27: 23.18 Modular Transformations
28: 30.4 Functions of the First Kind
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30.4.4
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►If is mean-square integrable on , then formally
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30.4.7
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30.4.9
►It is also equiconvergent with its expansion in Ferrers functions (as in (30.4.2)), that is, the difference of corresponding partial sums converges to 0 uniformly for .
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29: 19.31 Probability Distributions
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and occur as the expectation values, relative to a normal probability distribution in or , of the square root or reciprocal square root of a quadratic form.
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19.31.1
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