Turán Type inequalities for (p, q)-Gamma function
نویسنده
چکیده
have many applications in pure mathematics as in other branches of science. They are named by Karlin and Szegő in [8], Turán-type inequalities because the first of these type of inequalities was introduced by Turán in [18]. More precisely, he used some results of Szegő in [17] to prove the previous inequality for x ∈ (−1, 1), where fn is the Legendre polynomial of degree n. This classical result has been extended in many directions, as ultraspherical polynomials, Lagguere and Hermite polynomials, or Bessel functions, and so forth. Many results of Turán-type have been established on the zeros of special functions. Recently, W. T. Sulaiman in [15] proved some Turán-type inequalities for some q-special functions as well as the polygamma functions, by using the following inequality: Lemma 1.1. Let a ∈ R+ ∪ {∞} and let f and g be two nonnegative functions. Then ( a ∫
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Article history: Received 20 June 2008 Available online 22 August 2008 Submitted by B.C. Berndt
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