An Accurate Estimate of Mathieu’s Series

A New Lower Bound for Mathieu’s Series

In this paper, we establish a new lower bound for Mathieu’s series and present a simple and short proof of the Mathieu’s inequality. We also give a simple derivation of the integral form of the series.

Some New Bounds for Mathieu’s Series

Exact absorption probabilities for the D3-brane

We consider a minimal scalar in the presence of a three-brane in ten dimensions. The linearized equation of motion, which is just the wave equation in the three-brane metric, can be solved in terms of associated Mathieu functions. An exact expression for the reflection and absorption probabilities can be obtained in terms of the characteristic exponent of Mathieu’s equation. We describe an algo...

An Accurate Correlation to Estimate Saturated Molar Volume of Liquids

There are a number of techniques available to estimate saturated-liquid molar or specific volumes or densities of liquids. In this study, a new empirical correlation is presented to calculate volume of saturated liquids as a function of critical volume, reduced temperature and acentric factor. An optimization algorithm is utilized to obtain unknown parameters of this correlation by fitting them...

New upper bounds for Mathieu–type series

The Mathieu’s series S(r) was considered firstly by É.L. Mathieu in 1890; its alternating variant S̃(r) has been recently introduced by Pogány et al. [12] where various bounds have been established for S, S̃. In this note we obtain new upper bounds over S(r), S̃(r) with the help of Hardy–Hilbert double integral inequality. 2000 Mathematics Subject Classification. Primary: 26D15, 33E20.