An accurate approximation of zeta-generalized-Euler-constant functions

Vito Lampret

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Boyadzhiev, Khristo N. (2002)

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Some estimates for the first eigenvalue of the Sturm-Liouville problem with a weight integral condition

Maria Telnova (2012)

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Let $λ_{1} (Q)$ be the first eigenvalue of the Sturm-Liouville problem $y^{''} - Q (x) y + λ y = 0, y (0) = y (1) = 0, 0 < x < 1 .$ We give some estimates for $m_{α, β, γ} = {inf}_{Q \in T_{α, β, γ}} λ_{1} (Q)$ and $M_{α, β, γ} = {sup}_{Q \in T_{α, β, γ}} λ_{1} (Q)$ , where $T_{α, β, γ}$ is the set of real-valued measurable on $[0, 1]$ $x^{α} {(1 - x)}^{β}$ -weighted $L_{γ}$ -functions $Q$ with non-negative values such that $\int_{0}^{1} x^{α} {(1 - x)}^{β} Q^{γ} (x) d x = 1$ $(α, β, γ \in ℝ, γ \neq 0)$ .