A new type of sharp bounds for ratios of modified Bessel functions

By Diego Ruiz-Antolín, Javier Segura. 2016

49 citations recorded by the source corpus.

The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of parameters and which are shaper than previous bounds. The new bounds are obtained by a qualitative analysis of the Riccati equation satisfied by these ratios. A procedure is considered in which the bounds obtained from the analysis of the Riccati equation are used to define a new function satisfying a new Riccati equation which yields sharper bounds. Similar ideas can be applied to other functions.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8a5acd851a0454a909a8a633f591a7086cb2a975

Citations in the corpus

• Matching Normalizing Flows and Probability Paths on Manifolds (2022, unknown): “In particular (Ruiz-Antolı́n & Segura, 2016) suggest the following lower and upper bounds: ν − 12 + √ (ν + 12 ) 2 + κ2 κ > ive(ν − 1, κ) ive(ν, κ) > ν − 1 + √ (ν + 1)2 + κ2 κ Similar to (Oh et al., 2019) we take the average of the higher and lower bound (see (Oh et al., 2019) for empirically…”
• The Variance-Gamma Distribution: A Review (2023, unknown): “70) were derived by Segura [106] and Ruiz-Antoĺın and Segura [101], respectively.”