moment functionals

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1: Bibliography J

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Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function. In Orthogonal functions, moment theory, and continued fractions (Campinas, 1996), Lecture Notes in Pure and Appl. Math., Vol. 199, pp. 257–274.

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MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§5.10, §5.10.

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2: 18.34 Bessel Polynomials

… ►The full system satisfies orthogonality with respect to a (not positive definite) moment functional; see Evans et al. (1993, (2.7)) for the simple expression of the moments ${\mu }_n$. …

3: Bibliography D

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Functions with given moments and weight functions for orthogonal polynomials. Rocky Mountain J. Math. 23, pp. 87–104.

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ISSN 0035-7596, MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§18.34(ii).

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4: Bibliography L

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Moment integrals of powers of Airy functions. Z. Angew. Math. Phys. 44 (5), pp. 891–908.

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ISSN 0044-2275, Document, MathReview (B. M. Agrawal), ZentralBlatt

Referenced by:

(9.11.15), (9.11.18), §9.11(v), §9.11(v).

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5: 18.40 Methods of Computation

… ►Given the power moments, ${\mu }_n={\int }_a^b{x}^{n}d\mu (x)$, $n=0,1,2,\mathrm{\dots }$, can these be used to find a unique $\mu (x)$, a non-decreasing, real, function of $x$, in the case that the moment problem is determined? Should a unique solution not exist the moment problem is then indeterminant. …

6: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►and functions $f(x),g(x)\in C^2(a,b)$, assumed real for the moment. …

7: 18.39 Applications in the Physical Sciences

… ►The corresponding eigenfunction transform is a generalization of the Kontorovich–Lebedev transform §10.43(v), see Faraut (1982, §IV). … ►

a) Spherical Radial Coulomb Wave Functions Expressed in terms of Laguerre OP’s

►The functions ${\psi }_{p,l}(r)$ satisfy the equation, … ►

c) Spherical Radial Coulomb Wave Functions

… ►The equivalent quadrature weight, $w_i/w^{\mathrm{CP}}(x_i)$, also forms the foundation of a novel inversion of the Stieltjes–Perron moment inversion discussed in §18.40(ii). …

8: Bibliography G

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Integrals of three Bessel functions and Legendre functions. I. J. Math. Phys. 26 (4), pp. 633–644.

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ISSN 0022-2488, Document, MathReview (B. D. Agrawal), ZentralBlatt

Referenced by:

§10.22(iv), §10.43(iv).

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Integrals of three Bessel functions and Legendre functions. II. J. Math. Phys. 26 (4), pp. 645–655.

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ISSN 0022-2488, Document, MathReview (B. D. Agrawal), ZentralBlatt

Referenced by:

§10.22(iv), §10.43(iv).

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Mathieu functions. Trans. Camb. Philos. Soc. 23, pp. 303–336.

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External Links:

ZentralBlatt

Referenced by:

§28.26(i), §28.26(i), §28.8(iii).

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Matrices, moments and quadrature with applications. Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ.

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ISBN 978-0-691-14341-5, MathReview (G. A. Evans)

Referenced by:

§18.2(ix), §18.40(ii).

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Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions. Phys. Rev. E 47 (4), pp. R2233–R2236.

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Document

Referenced by:

§19.35(ii).

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9: Bibliography B

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Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions. Cambridge University Press, Cambridge.

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Notes:

Reprint of the 1897 original, with a foreword by Igor Krichever.

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ISBN 0-521-49877-5, MathReview (John B. Little), ZentralBlatt

Referenced by:

§20.9(ii).

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Automatic computation of zeros of Bessel functions and other special functions. SIAM J. Sci. Comput. 21 (4), pp. 1458–1464.

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ISSN 1064-8275, Document, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.74(vi), §3.8(iii).

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Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.

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Document

Referenced by:

§24.18.

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Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V. Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.

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ISSN 0080-4614, FullText, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§28.8(iv).

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Tables Relating to the Radial Mathieu Functions. Vol. 1: Functions of the First Kind. U.S. Government Printing Office, Washington, D.C..

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MathReview (C. J. Bouwkamp)

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1st item.

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10: Bibliography

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Computation of the regular confluent hypergeometric function. The Mathematica Journal 5 (4), pp. 74–76.

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ISSN 1047-5974, FullText

Referenced by:

§13.32(iii).

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Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions. J. Math. Physics 33, pp. 111–116.

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External Links:

MathReview (E. Weber), ZentralBlatt

Referenced by:

§33.9(ii).

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The classical moment problem and some related questions in analysis. Classics in Applied Mathematics, Vol. 82, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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Notes:

Reprint of the 1965 edition [ 0184042], Translated by N. Kemmer, With a foreword by H. J. Landau

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ISBN 978-1-611976-38-0, MathReview Entry

Referenced by:

§18.40(ii).

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Integrals involving Bickley and Bessel functions in radiative transfer, and generalized exponential integral functions. J. Heat Transfer 118 (3), pp. 789–792.

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Document

Referenced by:

§10.73(iv), §8.24(iii).

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Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J. Math. Anal. 23 (2), pp. 512–524.

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ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§19.9(i).

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