Journal of difference equations and applications, ISSN 1563-5120, 2017, Volume 24, Issue 3, pp. 425 - 437

We introduce a new class of discrete Bessel functions and discrete modified Bessel functions of integer order...

Bessel function | modified Bessel function | fundamental solution | Bessel difference equation | discrete diffusion equation | discrete wave equation | INTEGRALS | MATHEMATICS, APPLIED | SYSTEMS | Difference equations | Partial differential equations | Bessel functions | Wave equations

Bessel function | modified Bessel function | fundamental solution | Bessel difference equation | discrete diffusion equation | discrete wave equation | INTEGRALS | MATHEMATICS, APPLIED | SYSTEMS | Difference equations | Partial differential equations | Bessel functions | Wave equations

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 374, Issue 2, pp. 516 - 528

New sharp inequalities for the ratios of Bessel functions of consecutive orders are obtained using as main tool the first order difference-differential equations satisfied by these functions...

Riccati equation | Modified Bessel functions | Condition numbers | Bounds | Turán-type inequalities | MATHEMATICS | MATHEMATICS, APPLIED | FORM | PRODUCT | MONOTONICITY | Turan-type inequalities | VECTORS

Riccati equation | Modified Bessel functions | Condition numbers | Bounds | Turán-type inequalities | MATHEMATICS | MATHEMATICS, APPLIED | FORM | PRODUCT | MONOTONICITY | Turan-type inequalities | VECTORS

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 07/2013, Volume 33, Issue 3, pp. 1048 - 1062

A Green's-function-based solver for the modified Bessel equation has been developed with the primary motivation of solving the Poisson and biharmonic equations in cylindrical geometries...

biharmonic equation | Poisson equation | modified Bessel function | MATHEMATICS, APPLIED | SOLVER | ALGORITHM | Permissible error | Interpolation | Computation | Mathematical analysis | Decay | Solvers | Mathematical models | Bessel functions

biharmonic equation | Poisson equation | modified Bessel function | MATHEMATICS, APPLIED | SOLVER | ALGORITHM | Permissible error | Interpolation | Computation | Mathematical analysis | Decay | Solvers | Mathematical models | Bessel functions

Journal Article

Thermal Science, ISSN 0354-9836, 2018, Volume 22, Issue Suppl. 1, pp. S203 - S209

In thermal sciences, it is possible to encounter topics such as Bessel beams, Bessel functions or Bessel equations...

Discrete fractional calculus | Modified Bessel equation | Nabla operator | modified Bessel equation | nabla operator | THERMODYNAMICS | discrete fractional calculus

Discrete fractional calculus | Modified Bessel equation | Nabla operator | modified Bessel equation | nabla operator | THERMODYNAMICS | discrete fractional calculus

Journal Article

ACTA POLYTECHNICA HUNGARICA, ISSN 1785-8860, 2019, Volume 16, Issue 5, pp. 63 - 69

... the solution of a fourth-order linear homogeneous Bessel-type differential equation. Moreover, we point out that an inequality by Ashbaugh and Benguria as well...

contour integral | ENGINEERING, MULTIDISCIPLINARY | Hankel integral | Lagrange multipliers | asymptotics | fourth order differential equation | Bessel functions | modified Bessel functions | Wronski determinant

contour integral | ENGINEERING, MULTIDISCIPLINARY | Hankel integral | Lagrange multipliers | asymptotics | fourth order differential equation | Bessel functions | modified Bessel functions | Wronski determinant

Journal Article

Nonlinearity, ISSN 1361-6544, 2016, Volume 29, Issue 12, pp. 3857 - 3870

We investigate the question on existence of entire solutions of well-known linear differential equations that are linearizations of nonlinear equations modeling the Josephson effect in superconductivity...

ordinary differential equations on two-torus | phase-lock areas | 34M05 | rotation number | double confluent Heun equations | entire solutions | Josephson effect in superconductivity Mathematics Subject Classification numbers: 33C10 | modified Bessel functions | MATHEMATICS, APPLIED | JOSEPHSON-JUNCTION | MODEL | PHYSICS, MATHEMATICAL | Josephson effect in superconductivity | DYNAMICS | QUANTIZATION | Mathematics - Dynamical Systems

ordinary differential equations on two-torus | phase-lock areas | 34M05 | rotation number | double confluent Heun equations | entire solutions | Josephson effect in superconductivity Mathematics Subject Classification numbers: 33C10 | modified Bessel functions | MATHEMATICS, APPLIED | JOSEPHSON-JUNCTION | MODEL | PHYSICS, MATHEMATICAL | Josephson effect in superconductivity | DYNAMICS | QUANTIZATION | Mathematics - Dynamical Systems

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2014, Volume 142, Issue 6, pp. 2019 - 2025

In this note our aim is to determine the radius of starlikeness of the normalized Bessel functions of the first kind for three different kinds of normalization...

Circles | Mathematical theorems | Roots of functions | Modified Bessel functions | Mathematical functions | Bessel functions | Informatics | Equation roots | Starlike and convex functions | Bessel and modified Bessel functions of the first kind | Radius of starlikeness | Univalent | MATHEMATICS | univalent | MATHEMATICS, APPLIED | starlike and convex functions | radius of starlikeness

Circles | Mathematical theorems | Roots of functions | Modified Bessel functions | Mathematical functions | Bessel functions | Informatics | Equation roots | Starlike and convex functions | Bessel and modified Bessel functions of the first kind | Radius of starlikeness | Univalent | MATHEMATICS | univalent | MATHEMATICS, APPLIED | starlike and convex functions | radius of starlikeness

Journal Article

Advances in difference equations, ISSN 1687-1847, 2019, Volume 2019, Issue 1, pp. 1 - 14

This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions...

Ordinary Differential Equations | Functional Analysis | Analysis | Hypergeometric Function | Difference and Functional Equations | Kibble’s bivariate gamma distribution | Mathematics, general | Modified Bessel Function | Mathematics | Convexity | Partial Differential Equations | Concavity | RATIOS | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | BOUNDS | Kibble's bivariate gamma distribution | Bivariate analysis | Probability distribution functions | Bessel functions

Ordinary Differential Equations | Functional Analysis | Analysis | Hypergeometric Function | Difference and Functional Equations | Kibble’s bivariate gamma distribution | Mathematics, general | Modified Bessel Function | Mathematics | Convexity | Partial Differential Equations | Concavity | RATIOS | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | BOUNDS | Kibble's bivariate gamma distribution | Bivariate analysis | Probability distribution functions | Bessel functions

Journal Article

Expositiones Mathematicae, ISSN 0723-0869, 2015, Volume 33, Issue 2, pp. 223 - 251

... Turán type inequalities for modified Bessel functions of the first and second kinds are deduced...

Functional inequalities | Sharp bounds | Modified Bessel functions of the first and second kinds | Bessel functions of the first and second kinds | Turán-type inequalities | Product of modified Bessel functions | RATIOS | MISES-FISHER DISTRIBUTIONS | INEQUALITIES | PARAMETER-ESTIMATION | STABILITY | DIFFERENTIAL-EQUATIONS | MONOTONICITY | Turan-type inequalities | MATHEMATICS | 1ST | PRODUCTS | ARGUMENT

Functional inequalities | Sharp bounds | Modified Bessel functions of the first and second kinds | Bessel functions of the first and second kinds | Turán-type inequalities | Product of modified Bessel functions | RATIOS | MISES-FISHER DISTRIBUTIONS | INEQUALITIES | PARAMETER-ESTIMATION | STABILITY | DIFFERENTIAL-EQUATIONS | MONOTONICITY | Turan-type inequalities | MATHEMATICS | 1ST | PRODUCTS | ARGUMENT

Journal Article

International Journal of Heat and Mass Transfer, ISSN 0017-9310, 09/2018, Volume 124, pp. 74 - 82

....•The modified Bessel equation of zero order is transformed into a Cauchy-Euler equation.•Temperatures and heat transfer rates can be easily evaluated with high degrees of accuracy...

Transformed Cauchy-Euler equation | Approximate | Analytical temperatures and heat transfer rates of excellent quality | Modified Bessel equation of zero order | Rectangular annular fins | MECHANICS | THERMODYNAMICS | Analytical temperatures and heat transfer | rates of excellent quality | ENGINEERING, MECHANICAL | Mechanical engineering

Transformed Cauchy-Euler equation | Approximate | Analytical temperatures and heat transfer rates of excellent quality | Modified Bessel equation of zero order | Rectangular annular fins | MECHANICS | THERMODYNAMICS | Analytical temperatures and heat transfer | rates of excellent quality | ENGINEERING, MECHANICAL | Mechanical engineering

Journal Article

Results in Mathematics, ISSN 1422-6383, 9/2017, Volume 72, Issue 1, pp. 617 - 632

... (for all newly defined Bessel and Struve functions), complete monotonicity, Turán type inequality, associated non-homogeneous differential-difference equations...

Primary 33B15 | Bounding inequalities | 33C10 | Turán type inequality | 33E20 | ( $$p, q$$ p , q )-Extended Struve and modified Struve functions | Mathematics | Differential–difference equation | Complete monotonicity | 39B62 | Secondary 26A48 | Mathematics, general | ( $$p, q$$ p , q )-Extended beta function | Integral representation | ( $$p, q$$ p , q )-Extended Bessel and modified Bessel functions of the first kind | (p, q)-Extended Bessel and modified Bessel functions of the first kind | (p, q)-Extended Struve and modified Struve functions | (p, q)-Extended beta function | MATHEMATICS, APPLIED | Differential-difference equation | SERIES | POLYNOMIALS | MATHEMATICS | BOUNDS | Turan type inequality | ZEROS | Resveratrol

Primary 33B15 | Bounding inequalities | 33C10 | Turán type inequality | 33E20 | ( $$p, q$$ p , q )-Extended Struve and modified Struve functions | Mathematics | Differential–difference equation | Complete monotonicity | 39B62 | Secondary 26A48 | Mathematics, general | ( $$p, q$$ p , q )-Extended beta function | Integral representation | ( $$p, q$$ p , q )-Extended Bessel and modified Bessel functions of the first kind | (p, q)-Extended Bessel and modified Bessel functions of the first kind | (p, q)-Extended Struve and modified Struve functions | (p, q)-Extended beta function | MATHEMATICS, APPLIED | Differential-difference equation | SERIES | POLYNOMIALS | MATHEMATICS | BOUNDS | Turan type inequality | ZEROS | Resveratrol

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 12/2015, Volume 26, Issue 12, pp. 939 - 955

New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions...

Fourier transform | Bessel functions | modified Bessel functions | Kontorovich-Lebedev transform | index transforms | Mellin transform | Kontorovich–Lebedev transform | MATHEMATICS | MATHEMATICS, APPLIED | Partial differential equations | Fourier transforms | Operators (mathematics) | Kernels | Integrals | Transforms | Inversions | Fourier analysis | Initial value problems

Fourier transform | Bessel functions | modified Bessel functions | Kontorovich-Lebedev transform | index transforms | Mellin transform | Kontorovich–Lebedev transform | MATHEMATICS | MATHEMATICS, APPLIED | Partial differential equations | Fourier transforms | Operators (mathematics) | Kernels | Integrals | Transforms | Inversions | Fourier analysis | Initial value problems

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2016, Volume 305, pp. 217 - 243

We consider the numerical solution of the wave equation in a two-dimensional domain and start from a boundary integral formulation for its discretization...

Wave equation | Convolution quadrature | Modified Bessel function | Panel clustering | Boundary element method | DOMAIN | BOUNDARY INTEGRAL-EQUATIONS | ELEMENT METHOD | BEM | PHYSICS, MATHEMATICAL | RAPID SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TIME BIE METHOD | OPERATORS | DISCRETIZED OPERATIONAL CALCULUS | SCATTERING | Panels | Discretization | Mathematical analysis | Wave equations | Mathematical models | Boundaries | Clustering

Wave equation | Convolution quadrature | Modified Bessel function | Panel clustering | Boundary element method | DOMAIN | BOUNDARY INTEGRAL-EQUATIONS | ELEMENT METHOD | BEM | PHYSICS, MATHEMATICAL | RAPID SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TIME BIE METHOD | OPERATORS | DISCRETIZED OPERATIONAL CALCULUS | SCATTERING | Panels | Discretization | Mathematical analysis | Wave equations | Mathematical models | Boundaries | Clustering

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 09/2015, Volume 259, Issue 5, pp. 1967 - 1989

...⁎(∞). For our purpose the solutions to the model are formulated in the form of integral equations involving modified Bessel functions, for which new asymptotic estimates are provided. To the best of our knowledge, this is the first time that the classical Bessel functions are used to describe the solutions of lattice differential equations, and this approach possesses its own interest in further studying lattice differential equations.

Persistence | Lattice differential equation | Modified Bessel function | Spreading speed | EXISTENCE | SPEEDS | FAILURE | TRAVELING-WAVES | MATHEMATICS | SYSTEMS | ADVANCE | PROPAGATION | VEGETATION | Analysis | Differential equations

Persistence | Lattice differential equation | Modified Bessel function | Spreading speed | EXISTENCE | SPEEDS | FAILURE | TRAVELING-WAVES | MATHEMATICS | SYSTEMS | ADVANCE | PROPAGATION | VEGETATION | Analysis | Differential equations

Journal Article

Results in Physics, ISSN 2211-3797, 2017, Volume 7, pp. 3333 - 3343

Common recipe for the Lengthening Pendulum (LP) involves some change of variables to give a relationship with the Bessel’s equation...

Method of Modified Airy Function (MAF) | Initial value problems | The lengthening pendulum | Linear differential equations | Semiclassical approximation | TEST APPROXIMATION METHODS | PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | ASYMPTOTIC SOLUTIONS | EXACTLY SOLVABLE MODELS | MODIFIED AIRY FUNCTIONS | OPTICAL WAVE-GUIDES | ILLUSTRATE SUPERSYMMETRY | QUANTUM-MECHANICS | ORDINARY DIFFERENTIAL-EQUATIONS

Method of Modified Airy Function (MAF) | Initial value problems | The lengthening pendulum | Linear differential equations | Semiclassical approximation | TEST APPROXIMATION METHODS | PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | ASYMPTOTIC SOLUTIONS | EXACTLY SOLVABLE MODELS | MODIFIED AIRY FUNCTIONS | OPTICAL WAVE-GUIDES | ILLUSTRATE SUPERSYMMETRY | QUANTUM-MECHANICS | ORDINARY DIFFERENTIAL-EQUATIONS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2/2013, Volume 141, Issue 2, pp. 523 - 532

In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding...

Modified Bessel functions | Completely monotonic functions | Turán-type inequalities | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | PULSE DYNAMICS | completely monotonic functions | PRODUCTS | 3-COMPONENT SYSTEM | MONOTONICITY | Turan-type inequalities | 1ST KIND | ZEROS

Modified Bessel functions | Completely monotonic functions | Turán-type inequalities | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | PULSE DYNAMICS | completely monotonic functions | PRODUCTS | 3-COMPONENT SYSTEM | MONOTONICITY | Turan-type inequalities | 1ST KIND | ZEROS

Journal Article

17.
Full Text
Inequalities for integrals of modified Bessel functions and expressions involving them

Journal of mathematical analysis and applications, ISSN 0022-247X, 2018, Volume 462, Issue 1, pp. 172 - 190

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind...

Modified Bessel function | Integral | Inequality | RATIOS | MATHEMATICS | STEINS METHOD | MATHEMATICS, APPLIED | SEQUENCES | BOUNDS | PRODUCT

Modified Bessel function | Integral | Inequality | RATIOS | MATHEMATICS | STEINS METHOD | MATHEMATICS, APPLIED | SEQUENCES | BOUNDS | PRODUCT

Journal Article

Mathematical and Computer Modelling, ISSN 0895-7177, 03/2013, Volume 57, Issue 5-6, pp. 1298 - 1311

...–Emden differential equations. The method is based on the improvement of the Bessel polynomial solutions with the aid of the residual error function...

Bessel functions of the first kind | Approximation solution | Lane–Emden differential equations | Bessel collocation method | Modified Bessel collocation method | Lane-Emden differential equations | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | SINGULAR IVPS | ALGORITHM | SYSTEMS | INTEGRODIFFERENTIAL EQUATIONS | Analysis | Methods | Differential equations

Bessel functions of the first kind | Approximation solution | Lane–Emden differential equations | Bessel collocation method | Modified Bessel collocation method | Lane-Emden differential equations | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | SINGULAR IVPS | ALGORITHM | SYSTEMS | INTEGRODIFFERENTIAL EQUATIONS | Analysis | Methods | Differential equations

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 1232 - 1246

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...

Modified Bessel functions | Bounds | MATHEMATICS | MATHEMATICS, APPLIED

Modified Bessel functions | Bounds | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 11/2013, Volume 141, Issue 3, pp. 254 - 281

It is known that the Struve function H ν and the modified Struve function L ν are closely connected to the Bessel function of the first kind J ν...

Bessel function and modified Bessel function of the first kind | 40H05 | 33C10 | generalized hypergeometric function | 33E20 | 30B50 | Mathematics | Struve differential equation | Cahen formula | 65B10 | Neumann, Kapteyn and Schlömilch series of modified Bessel and Struve functions | 40C10 | Mathematics, general | modified Struve function | Dirichlet series | INEQUALITIES | Kapteyn and Schlomilch series of modified Bessel and Struve functions | OMEGA-FUNCTION | BESSEL-FUNCTIONS | MATHEMATICS | Neumann | ZETA-FUNCTION | 1ST | WAVES | MATHIEU A-SERIES | Mathematics - Classical Analysis and ODEs

Bessel function and modified Bessel function of the first kind | 40H05 | 33C10 | generalized hypergeometric function | 33E20 | 30B50 | Mathematics | Struve differential equation | Cahen formula | 65B10 | Neumann, Kapteyn and Schlömilch series of modified Bessel and Struve functions | 40C10 | Mathematics, general | modified Struve function | Dirichlet series | INEQUALITIES | Kapteyn and Schlomilch series of modified Bessel and Struve functions | OMEGA-FUNCTION | BESSEL-FUNCTIONS | MATHEMATICS | Neumann | ZETA-FUNCTION | 1ST | WAVES | MATHIEU A-SERIES | Mathematics - Classical Analysis and ODEs

Journal Article

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