The paper establishes uniform endpoint majorants for integrals ∫_0^x e^{-γ t} w(t) t^{-μ} I_μ(t) dt ≤ C e^{-γ x} w(x) x^{-μ} I_{μ+1}(x) under monotonicity conditions on w, resolving Gaunt's open problem for 0<γ<1.
Inequalities for modified Bessel functions
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Weighted Uniform Endpoint Majorants for Integrals Involving Modified Bessel Functions
The paper establishes uniform endpoint majorants for integrals ∫_0^x e^{-γ t} w(t) t^{-μ} I_μ(t) dt ≤ C e^{-γ x} w(x) x^{-μ} I_{μ+1}(x) under monotonicity conditions on w, resolving Gaunt's open problem for 0<γ<1.