Haar%20measure
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21—30 of 126 matching pages
21: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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22: 33.24 Tables
23: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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The supports of measures associated with orthogonal polynomials and the spectra of the related selfadjoint operators.
Rocky Mountain J. Math. 21 (1), pp. 501–527.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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24: 1.1 Special Notation
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real variables. | |
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the space of all Lebesgue–Stieltjes measurable functions on which are square integrable with respect to . | |
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25: 27.15 Chinese Remainder Theorem
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►Their product has 20 digits, twice the number of digits in the data.
…These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result , which is correct to 20 digits.
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26: William P. Reinhardt
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
27: 18.36 Miscellaneous Polynomials
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►These are OP’s on the interval with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at and to the weight function for the Jacobi polynomials.
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►These are polynomials in one variable that are orthogonal with respect to a number of different measures.
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►These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line.
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►This infinite set of polynomials of order , the smallest power of being in each polynomial, is a complete orthogonal set with respect to this measure.
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►Exceptional type I -EOP’s, form a complete orthonormal set with respect to a positive measure, but the lowest order polynomial in the set is of order , or, said another way, the first polynomial orders, are missing.
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28: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Extremal measures for a system of orthogonal polynomials.
Constr. Approx. 9, pp. 111–119.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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29: 6.19 Tables
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Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
30: Peter L. Walker
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