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moment functionals


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1: 18.34 Bessel Polynomials
Orthogonality can also be expressed in terms of moment functionals; see Durán (1993), Evans et al. (1993), and Maroni (1995). …
2: Bibliography J
  • W. B. Jones and W. Van Assche (1998) 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.
  • 3: Bibliography D
  • A. J. Durán (1993) Functions with given moments and weight functions for orthogonal polynomials. Rocky Mountain J. Math. 23, pp. 87–104.
  • 4: Bibliography L
  • B. J. Laurenzi (1993) Moment integrals of powers of Airy functions. Z. Angew. Math. Phys. 44 (5), pp. 891–908.
  • 5: Bibliography B
  • H. F. Baker (1995) Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions. Cambridge University Press, Cambridge.
  • J. S. Ball (2000) Automatic computation of zeros of Bessel functions and other special functions. SIAM J. Sci. Comput. 21 (4), pp. 1458–1464.
  • L. E. Ballentine and S. M. McRae (1998) Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.
  • W. Barrett (1981) 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.
  • G. Blanch and D. S. Clemm (1962) Tables Relating to the Radial Mathieu Functions. Vol. 1: Functions of the First Kind. U.S. Government Printing Office, Washington, D.C..
  • 6: Bibliography W
  • E. L. Wachspress (2000) Evaluating elliptic functions and their inverses. Comput. Math. Appl. 39 (3-4), pp. 131–136.
  • P. L. Walker (1991) Infinitely differentiable generalized logarithmic and exponential functions. Math. Comp. 57 (196), pp. 723–733.
  • P. L. Walker (2012) Reduction formulae for products of theta functions. J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
  • G. N. Watson (1910) The cubic transformation of the hypergeometric function. Quart. J. Pure and Applied Math. 41, pp. 70–79.
  • J. Wishart (1928) The generalised product moment distribution in samples from a normal multivariate population. Biometrika 20A, pp. 32–52.
  • 7: Bibliography C
  • B. C. Carlson (1985) The hypergeometric function and the R -function near their branch points. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 63–89.
  • B. C. Carlson (2006b) Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric R -functions. Math. Comp. 75 (255), pp. 1309–1318.
  • J. S. Christiansen and M. E. H. Ismail (2006) A moment problem and a family of integral evaluations. Trans. Amer. Math. Soc. 358 (9), pp. 4071–4097.
  • R. Cicchetti and A. Faraone (2004) Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics. IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
  • A. P. Clarke and W. Marwood (1984) A compact mathematical function package. Australian Computer Journal 16 (3), pp. 107–114.