Stieltjes%20constants
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1: 31.15 Stieltjes Polynomials
§31.15 Stieltjes Polynomials
… ►§31.15(ii) Zeros
… ►This is the Stieltjes electrostatic interpretation. … ►§31.15(iii) Products of Stieltjes Polynomials
…2: 18.40 Methods of Computation
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§18.40(ii) The Classical Moment Problem
… ►Having now directly connected computation of the quadrature abscissas and weights to the moments, what follows uses these for a Stieltjes–Perron inversion to regain . ►Stieltjes Inversion via (approximate) Analytic Continuation
… ►Histogram Approach
… ►Derivative Rule Approach
…3: 25.2 Definition and Expansions
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25.2.4
►where the Stieltjes constants
are defined via
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25.2.5
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25.2.12
►product over zeros of with (see §25.10(i)); is Euler’s constant (§5.2(ii)).
4: 2.6 Distributional Methods
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§2.6(ii) Stieltjes Transform
… ►The Stieltjes transform of is defined by … ►For a more detailed discussion of the derivation of asymptotic expansions of Stieltjes transforms by the distribution method, see McClure and Wong (1978) and Wong (1989, Chapter 6). Corresponding results for the generalized Stieltjes transform …An application has been given by López (2000) to derive asymptotic expansions of standard symmetric elliptic integrals, complete with error bounds; see §19.27(vi). …5: 25.6 Integer Arguments
6: 1.4 Calculus of One Variable
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Stieltjes, Lebesgue, and Lebesgue–Stieltjes integrals
… ► … ► … ► … ► See Riesz and Sz.-Nagy (1990, Ch. 3). …7: 1.14 Integral Transforms
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§1.14(vi) Stieltjes Transform
►The Stieltjes transform of a real-valued function is defined by … … ►Inversion
… ►Laplace Transform
…8: Bibliography R
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (4), pp. 91.
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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (3), pp. 56–64.
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A proof of the asymptotic series for log and log
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Ann. of Math. (2) 32 (1), pp. 10–16.
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9: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Zeros of Stieltjes and Van Vleck polynomials and applications.
J. Math. Anal. Appl. 110 (2), pp. 327–339.
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Zeros of Stieltjes and Van Vleck polynomials.
Trans. Amer. Math. Soc. 252, pp. 197–204.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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