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On the distributions of the densities involving non-zero zeros of bessel and legendre functions and their infinite divisibility.

  • Kumar, Hemant [2] ; Pathan, Mahmood Ahmad [1] ; Chandel, R. C. Singh [2]
    1. [1] University of Botswana

      University of Botswana

      Botsuana

    2. [2] D.A-V. College.
  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 29, Nº. 3, 2010, págs. 165-182
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172010000300001
  • Enlaces
  • Resumen
    • In the present paper, we introduce the probability density functions involving non-zero zeros of the Bessel and Legendre functions. Then, we evaluate the distributions of the characteristic functions defined by these probability density functions and again obtain their related functions and polynomials. Finally, we prove the infinite divisibility of these probability density functions.

  • Referencias bibliográficas
    • Citas [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publication, New York, (1970).
    • [2] L. Bondesson, On the infinite divisibility of the half-Cauchy and other decreasing densities and probability functions on the non-negative...
    • [3] M. J. Goovaerts, L. D Hooge and N. De, Pril, On the infinite divisibility of the product of two Γ-distributed stochastically variables,...
    • [4] H. Hochstadt, The Functions of Mathematical Physics, New York, Dover, (1986).
    • [5] D. H. Kelkar, Infinite divisibility and variance mixtures of the normal distribution, Ann. Math. Statistic. 42, pp. 802-808, (1971).
    • [6] H. Kumar and S. Srivastava, On some sequence of integrals and their applications, Bull. Cal. Math. Soc. 100 (5), pp. 563-572, (2008).
    • [7] K. Sato, Class L of multivariate distributions and its sub classes, J. Multivaria. Anal. 10 (1980), pp. 207-232, (1980).
    • [8] F. W. Steutel, Preservation of infinite divisibility under mixing and related topics, Math. Center, Tract. Amsterdam, 33, (1970).
    • [9] K. Takano, On a family of polynomials with zeros outside the unit disk, Int. J. Comput. Num. Anal. Appl. 1 (4), pp. 369-382, (2002).
    • [10] K. Takano, On the infinite divisibility of normed conjugate product of Gamma function, Proc. of 4th Int. Conf. SSFA, (4), pp. 1-8, (2003).
    • [11] O. Thorin, On the infinite divisibility of the Pareto distribution, Scand. Acturial. J. pp. 31-40, (1977)

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