Computation of modified Bessel functions and their ratios

Abstract

Abstract. An efficient algorithm for calculating ratios rv(x) = I,+,(x)/IAx), v â 0, x ä 0, is presented. This algorithm in conjunction with the recursion relation for rAx) gives an alternative to other recursive methods for I Ax) when approximations for low-order Bessel functions are available. Sharp bounds on r,(x) and IAx) are also established in addition to some monotonicity properties of ry(x) and r,'(x).

Sharp Bounds for the Ratio of Modified Bessel Functions

“…Amos in 1974 first showed the bounds G p,q (x) for the ratio R ν (x) (cf. formulas (11) and (16) in [3]) that for x, ν ≥ 0 there hold G ν+1,ν+1 (x) < R ν (x) < G ν,ν+2 (x) , (1.5) G ν+1/2,ν+3/2 (x) < R ν (x) < G ν+1/2,ν+1/2 (x) .…”

Adaptive control strategies and dependence of finite time ruin on the premium loading

“…Proof of Lemma 5.3. This assertion is a particular case (for integer n) of the inequality (16) in [2].…”

Lattice gauge theory without link variables

“…The accurate computation [21] of modified Bessel functions in (2.25) and their ratios in (3.2) and (3.5), for large J l , is essential to obtain the correct expectation value of 0-link observables in the SU(2) gauge theory. For SU(3), the effective link is constructed numerically with a simple Monte Carlo averaging.…”