Inequalities for modified Bessel functions and their integrals

By Robert E. Gaunt. 2012

84 citations recorded by the source corpus.

Abstract Simple inequalities for some integrals involving the modified Bessel functions I ν ( x ) and K ν ( x ) are established. We also obtain a monotonicity result for K ν ( x ) and a new lower bound, that involves gamma functions, for K 0 ( x ) .

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/4108ba8bb9ab5e828da6e023f1a91f66f00f7efb

Citations in the corpus

• Life-span of semilinear wave equations with scale-invariant damping: Critical Strauss exponent case (2017, unknown): “We collect some facts about Kν(t) from [10].”
• The Variance-Gamma Distribution: A Review (2023, unknown): “Upper and lower bounds for F (x) and F (x) can be obtained by using bounds of Gaunt [37, 39] for the integral ∫∞ x e tKν(t) dt, x > 0, −1 < β < 1, ν > −1/2.”