engleski

Some improvements over Love's inequality for the Laguerre function

Love's bounding inequalities for Laguerre functions $L_\nu^\mu(x)$ are significantly improved by two different methods in the real domain. The first method takes Luke's exponential inequalities for the confluent hypergeometric $\Phi \equiv \, _1F_1$, while the second approach explores the upper bounds for the first kind Bessel function $J_\mu(x)$ by Landau, and Olenko's now-a-days derived bound for the same special function. Finally, we deduce a bounding function for $L_\nu^\mu(x)$ combining Krasikov's uniform bound for Bessel functions with Olenko's result.

Bessel function of first kind $J_\mu(x)$; confluent hypergeometric $\; _1F_1$; Krasikov's uniform bound for $J_\mu(x)$; Laguerre function $L_\nu^\mu(x)$; Landau inequalities for $J_\mu(x)$; Love's inequalities; Luke's bounds on $\; _1F_1$; Olenko's bound

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