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  Volume 6, Issue 4, Article 126
Inequalities Involving Generalized Bessel Functions

    Authors: Árpád Baricz, Edward Neuman,  
    Keywords: Askey's inequality, Grünbaum's inequality, Bessel functions, Gegenbauer polynomials.  
    Date Received: 17/09/05  
    Date Accepted: 22/09/05  
    Subject Codes:

33C10, 26D20.

    Editors: Alexandru Lupas (1942-2007),  

Let $ u_p$ denote the normalized, generalized Bessel function of order $ p$ which depends on two parameters $ b$ and $ c$ and let $ lambda_p(x) = u_p(x^2)$ , $ x ge 0$. It is proven that under some conditions imposed on $ p$, $ b$, and $ c$ the Askey inequality holds true for the function $ lambda_p$, i.e., that $ lambda_p(x) + lambda_p(y) le 1 + lambda_p(z)$, where $ x,y ge 0$ and $ z^2 = x^2 + y^2$. The lower and upper bounds for the function $ lambda_p$ are also established.

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