On Turán's type inequalities for some special functions and operators.
DOI:
https://doi.org/10.4067/S0716-09172010000200002Keywords:
Turanians, negapolygamma function, generalized Hurwitz-Lerch Zeta function, Mellin transforms, unified Riemann zeta function, Riemann-Liouville fractional integral operator, turanianas, función negapoligamma, función zeta generalizada de Hurwitz-Kerch.Abstract
The purpose of this paper is to use the generalized Schwarz inequality to give a short proofs of new Turán-type inequalities for some special functions and operators.References
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Elbert Á., Laforgia, A. Some monotonicity properties for the zeros of ultraspherical polynomials, Acta Math. Hung., 48, pp. 155-159, (1986).
Laforgia, A. Sturm theory for certain class of Sturm-Liouville Equations and Turánians and Wronskians for the zero of derivative of Bessel functions, Indag. Math., 3, pp. 295-301, (1982).
Lorch, L. Turánians and Wronskians for the zeros of Bessel functions, SIAM J. Math.Anal.,11, pp. 223-227, (1980).
Szegö, G. Orthogonal Polynomial 4th ed. Amer. Math. Soc., Colloquium Publications,23 Amer. Math. Soc. Providence, RI (1975).
Szegö, G. On an inequality of P. Turán concerning Lengendre Polynomials,Bull Amer. Math. Soc., 54, pp. 401-405, (1948).
Goyal, S. P., Parashar, A. Some results for the unified Riemann zeta function, Kyungpook mathematical journal,42(1), pp. 87-94, (2002).
Miller, K.S., Ross, B. An introduction to the Fractional calculus and Fractional Differential equations, John wiley Sons, Inc. New York, (1993).
Adamchik, V. Polygamma function of negative order, Jour. Comp.Appl. Math., 100, pp. 191-199, (1998).
Rainville, E.D. Special functions, Chelsea Publ. Co. Bronx,New York, 1971).
Sneddon, I. N. The use of integral transforms, Mc-Graw Hill, New York., (1972).
Garg, M., Jain, K., Kalla, S. L. On Generalized Hurwitz-Lerch Zeta functions, Appl. and Appl. Math., 4(1), pp. 26-39, (2009).
Published
2011-01-07
How to Cite
[1]
H. S. Parihar, “On Turán’s type inequalities for some special functions and operators.”, Proyecciones (Antofagasta, On line), vol. 29, no. 2, pp. 93-100, Jan. 2011.
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