### Abstract

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

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Journal of Inequalities in Pure and Applied Mathematics |

Volume | 6 |

Issue number | 4 |

Publication status | Published - Nov 29 2005 |

### Keywords

- Askey's inequality
- Bessel functions
- Gegenbauer polynomials
- Grünbaum's inequality

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Árpád, B., & Neuman, E. (2005). Inequalities involving generalized bessel functions.

*Journal of Inequalities in Pure and Applied Mathematics*,*6*(4), 1-9.