Some improvements over Love's inequality for the Laguerre function

Dedicated to the Memories of Eric Russell Love (1912–2001) and Yudell Leo Luke (1918–1983)

Abstract

In the present article, Love's bounding inequalities for the Laguerre function are significantly improved by two different methods in the real domain. The first method is based upon Luke's exponential inequalities for the confluent hypergeometric function Φ ≡₁ F ₁, while the second approach explores the upper bounds for the first-kind Bessel function J _μ(x) by Landau, and Olenko's recently derived bound for the same Bessel function. Finally, we deduce a bounding function for combining Krasikov's uniform bound for the Bessel functions with Olenko's result cited above.

Dedicated to the Memories of Eric Russell Love (1912–2001) and Yudell Leo Luke (1918–1983)

Keywords:

• Bessel function of the first kind
• Confluent hypergeometric function
• Krasikov's uniform bound for the Bessel function
• Laguerre function
• Landau's inequalities for the Bessel function
• Love's inequalities
• Luke's bound for the confluent hypergeometric function
• Olenko's bound for the Bessel function

Acknowledgements

The present investigation was supported by the Ministry of Sciences, Education and Sports of Croatia under Research Project Number 112-2352818-2814 and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.

Notes

Dedicated to the Memories of Eric Russell Love (1912–2001) and Yudell Leo Luke (1918–1983)