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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.29 no.3 Antofagasta Dec. 2010

http://dx.doi.org/10.4067/S0716-09172010000300001 

Proyecciones Journal of Mathematics
Vol. 29, N° 3, pp. 165-182, December 2010.
Universidad Católica del Norte
Antofagasta - Chile


ON THE DISTRIBUTIONS OF THE DENSITIES INVOLVING NON-ZERO ZEROS OF BESSEL AND LEGENDRE FUNCTIONS AND THEIR INFINITE DIVISIBILITY


Hemant Kumar1
M. A. Pathan2
R. C. Singh Chandel3

1D. A-V. P. G. College Kanpur, India
2University Of Botswana, Botswana
3D. V. P. G. College Orai, India



Correspondencia a:


Abstract

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.

2000 Mathematics Subject Classification : 33C20, 62E15, 60E05, 60E10.

Keywords and Phrases : Probability density functions, characteristic functions, non zero zeros of Bessel and Legendre functions, infinite divisibility.



References

[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 line, Scand. Acturial J., pp. 225-247, (1985).

[3] M. J. Goovaerts, L. D Hooge and N. De, Pril, On the infinite divisibility of the product of two G-distributed stochastically variables, AppliedMathematics and Computation, 3, pp. 127-135, (1977).

[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).

Hemant Kumar
Department of Mathematics
D. A-V. P. G., College
Kanpur, U. P
India
e-mail : palhemant2007@rediffmail.com


M. A. Pathan
Department of Mathematics
University of Botswana
Gaborone
Botswana
e-mail : mapathan@gmail.com


R. C. Singh Chandel
Department of Mathematics
D. V. P. G., College
Orai, U. P
India
e-mail : rcschandel@yahoo.co.in


Received : September 2009. Accepted : January 2010

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