Abstract An approach to the generalized Bessel–Maitland function is proposed in present paper. It denoted by $\mathcal{J}_{\nu , \lambda }^{\mu }$ Jν,λμ where $\mu >0$ xmlns:mml="http://www.w3....

The paper presents the derivation of asymptotic behavior $\nu$-zeros modified Bessel function imaginary order $K_{{\rm i}\nu}(z)$. This is based on quasiclassical treatment exponential potential positive half axis. expression for (zeros with respect to order) contains Lambert $W$ function, which readily available in most computer algebra systems and numerical software packages. use this provide...

Bounds for the distance |cν,s− cν±1,s′ | between adjacent zeros of cylinder functions are given; s and s′ are such that @cν,s′′ ∈ ]cν,s, cν±1,s′ [; cν,k stands for the kth positive zero of the cylinder (Bessel) function Cν(x) = cosαJν(x)− sinαYν(x), α ∈ [0, π[, ν ∈ R. These bounds, together with the application of modified (global) Newton methods based on the monotonic functions fν(x) = x2ν−1Cν...

We denote by Iν and Kν the Bessel functions of the first and third kind, respectively. Motivated by the relevance of the function wν t t Iν−1 t /Iν t , t > 0, in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector 1984 , we establish new inequalities for Iν t /Iν−1 t . The results are based on the recurrence relations for Iν and Iν−1 and the ...