19 citations · 127 across the 51 of their papers we have counts for
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Sharp two-sided bounds for the product of modified Bessel functions and for its logarithmic derivative
Javier Segura, Soichiro Suzuki
We prove that, for all , the product of modified Bessel functions satisfies \[ \frac{1}{2\sqrt{x^2+ν^2+1/5}}<I_ν(x)K_ν(x)<\frac{1}{2\sqrt{x^2+ν^2-1/4}} , \] where the lower…
Optimized bounds for the product and the ratios of modified Bessel functions
Javier Segura, Soichiro Suzuki
New sharp bounds for the product and the ratios of modified Bessel functions are presented. Most bounds for the product are derived as direct consequences of previously established…
McMahon-type asymptotic expansions of the zeros of the Coulomb wave functions
Amparo Gil, Javier Segura, Nico M. Temme
We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions…
Simple bounds with best possible accuracy for ratios of modified Bessel functions
J. Segura
The best bounds of the form for ratios of modified Bessel functions are characterized: if , and are chosen in such a way that $B(α,…
Complete asymptotic expansions for the relativistic Fermi-Dirac integral
A. Gil, J. Segura, N. M. Temme
Fermi-Dirac integrals appear in problems in nuclear astrophysics, solid state physics or in the fundamental theory of semiconductor modeling, among others areas of application. In…
Monotonicity properties for ratios and products of modified Bessel functions and sharp trigonometric bounds
Javier Segura
Let and be the first and second kind modified Bessel functions. It is shown that the nullclines of the Riccati equation satisfied by , , wi…