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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2: 18.34 Bessel Polynomials
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►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
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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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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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5: 18.40 Methods of Computation
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►Given the power moments, , , can these be used to find a unique , a non-decreasing, real, function of , in the case that the moment problem is determined? Should a unique solution not exist the moment problem is then indeterminant.
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6: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
7: 18.39 Applications in the Physical Sciences
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►The corresponding eigenfunction transform is a generalization of the Kontorovich–Lebedev transform §10.43(v), see Faraut (1982, §IV).
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a) Spherical Radial Coulomb Wave Functions Expressed in terms of Laguerre OP’s
►The functions satisfy the equation, … ►c) Spherical Radial Coulomb Wave Functions
… ►The equivalent quadrature weight, , 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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Integrals of three Bessel functions and Legendre functions. II.
J. Math. Phys. 26 (4), pp. 645–655.
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Mathieu functions.
Trans. Camb. Philos. Soc. 23, pp. 303–336.
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Matrices, moments and quadrature with applications.
Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ.
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Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions.
Phys. Rev. E 47 (4), pp. R2233–R2236.
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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Automatic computation of zeros of Bessel functions and other special functions.
SIAM J. Sci. Comput. 21 (4), pp. 1458–1464.
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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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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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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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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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Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions.
J. Math. Physics 33, pp. 111–116.
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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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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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Functional inequalities for hypergeometric functions and complete elliptic integrals.
SIAM J. Math. Anal. 23 (2), pp. 512–524.
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