Results 51 to 60 of about 27,421 (244)

Polynomial approximations to Bessel functions [PDF]

IEEE Transactions on Antennas and Propagation, 2003
A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order ...
Millane, R.P., Eads, J.L.
openaire   +1 more source

Advances in Mode (De)Multiplexing Technologies via Circularly Symmetric Structured Light Beams

Advanced Photonics Research, EarlyView.
This review presents a comprehensive overview of mode (de)multiplexing technologies using circularly symmetric structured light beams, encompassing strategies of beam splitter combinations, multiorder diffractive gratings, optical coordinate transformations, angular dispersion lenses, multilayer cascaded modulations, and multidimensional hybrid (de ...
Qingji Zeng, Shu Chen, Zhibin Wu, Junmin Liu, Huapeng Ye, Gaiqing Zhao, Dianyuan Fan, Shuqing Chen   +7 more
wiley   +1 more source

Infinite Series Based on Bessel Zeros

Applied Sciences, 2023
An interesting series based on Bessel function roots (zeros) is discussed and numerically analyzed. The novel-derived simplified general solutions are based on Lommel polynomials.
Kamil Urbanowicz
doaj   +1 more source

On the zeros of Bessel polynomials

Journal of Approximation Theory, 1985
AbstractA closed expression for the reciprocal power sums of the difference of zeros of Bessel polynomials is derived using elementary complex analysis. These are sums of the form ∑k=1k≠jn(xj−xk)−m; m=1,2..., where xj are the zeros of a Bessel polynomial. Recurrence formulae for sums ∑i − 1n xj−m and ∑i − 1n xjm are also established.
openaire   +2 more sources

Low‐Energy Atomic Scattering: S‐Wave Relation Between the Interaction Potential and the Phase Shift

Annalen der Physik, EarlyView.
The validity of the on‐shell approximation for s‐wave scattering is examined across one, two, and three dimensions using exactly solvable model interaction potentials. By comparing exact and approximate s‐wave components of the interaction potential, the analysis reveals that the approximation improves with increasing momentum and decreasing ...
Francesco Lorenzi, Luca Salasnich
wiley   +1 more source

APPLICATION OF THE BESSEL-HYBRID FUNCTIONS FOR THE LINEAR FREDHOLM-VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS [PDF]

Romanian Journal of Mathematics and Computer Science, 2015
In this paper a collocation method based on the Bessel-hybrid functions is used for approximation of the solution of linear Fredholm-Volterra integro-differential equations (FVIDEs) under mixed conditions.
YADOLLAH ORDOKHANI, HANIYE DEHESTANI
doaj  

Real orthogonalizing weights for Bessel polynomials

Journal of Computational and Applied Mathematics, 1993
AbstractWe construct real orthogonalizing weights of bounded variation for the generalized Bessel polynomials.
EVANS, WD, EVERITT, WN, KWON, KH Kwon, Kil Hyun, LITTLEJOHN, LL   +3 more
openaire   +2 more sources

Boundary conditions and universal finite‐size scaling for the hierarchical |φ|4$|\varphi |^4$ model in dimensions 4 and higher

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We analyse and clarify the finite‐size scaling of the weakly‐coupled hierarchical n$n$‐component |φ|4$|\varphi |^4$ model for all integers n≥1$n \ge 1$ in all dimensions d≥4$d\ge 4$, for both free and periodic boundary conditions. For d>4$d>4$, we prove that for a volume of size Rd$R^{d}$ with periodic boundary conditions the infinite‐volume ...
Emmanuel Michta, Jiwoon Park, Gordon Slade   +2 more
wiley   +1 more source

The orthogonal polynomials generated by [ceteris omissis] [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 1995
Starting from the generating function, a differential-recurrence relation is derived, which is then combined with the three-term pure recurrence formula (a necessary and sufficient condition for orthogonal polynomials) to obtain a differential ...
A.L.W. VON BACHHAUS
doaj  

Central factorials under the Kontorovich-Lebedev transform of polynomials

, 2012
We show that slight modifications of the Kontorovich-Lebedev transform lead to an automorphism of the vector space of polynomials. This circumstance along with the Mellin transformation property of the modified Bessel functions perform the passage of ...
Abramowitz M., Ana F. Loureiro, Ben Cheikh Y., Butzer P. L., Charalambides Ch. A., Chihara T. S., Cigler J., Erdélyi A., Gelineau Y., Gessel I. M., Kontorovich M. I., Lebedev N. N., Lebedev N. N., Liu G. D., Loureiro A. F., Maroni P., Olver F. W., Prudnikov A. P., S. Yakubovich, Sloane N. J., Sneddon I. N., Van Iseghem J., Yakubovich S. B., Zhang W.   +23 more
core   +1 more source