scholarly journals Closed-form expressions for derivatives of Bessel functions with respect to the order

2018 ◽  
Vol 466 (1) ◽  
pp. 1060-1081 ◽  
Author(s):  
J.L. González-Santander
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Derivatives Of

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

ASYMPTOTICS OF ZEROS OF CERTAIN ENTIRE FUNCTIONS

2007 ◽  
Vol 05 (03) ◽  
pp. 291-299
Author(s):  
MOURAD E. H. ISMAIL
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Entire Functions

We derive representations for some entire q-functions and use it to derive asymptotics and closed form expressions for large zeros of a class of entire functions including the Ramanujan function, and q-Bessel functions.

scholarly journals On the integral kernels of derivatives of the Ornstein–Uhlenbeck semigroup

2016 ◽  
Vol 19 (04) ◽  
pp. 1650030 ◽  
Author(s):  
Jonas Teuwen
Keyword(s):  
Closed Form ◽  
Hermite Polynomials ◽  
Closed Form Expression ◽  
Alternative Proof ◽  
Kernel Estimates ◽  
Form Expression ◽  
Mehler Kernel ◽  
Derivatives Of

This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein–Uhlenbeck semigroup [Formula: see text]. Our approach is to expand the Mehler kernel into Hermite polynomials and apply the powers [Formula: see text] of the Ornstein–Uhlenbeck operator to it, where we exploit the fact that the Hermite polynomials are eigenfunctions for [Formula: see text]. As an application we give an alternative proof of the kernel estimates by Ref. 10, making all relevant quantities explicit.

On the zeros of derivatives of Bessel functions

1983 ◽  
Vol 34 (6) ◽  
pp. 774-786 ◽  
Author(s):  
�rp�d Elbert ◽  
Andrea Laforgia
Keyword(s):  
Bessel Functions ◽  
Derivatives Of ◽  
Zeros Of Derivatives

scholarly journals A Review of Procedures for Summing Kapteyn Series in Mathematical Physics

2009 ◽  
Vol 2009 ◽  
pp. 1-34 ◽  
Author(s):  
R. C. Tautz ◽  
I. Lerche
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Mathematical Physics ◽  
Short Review ◽  
Quantum Systems ◽  
Review Article ◽  
Functional Behavior ◽  
Basic Physics ◽  
Kapteyn Series ◽  
Physics Problems

Since the discussion of Kapteyn series occurrences in astronomical problems the wealth of mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the structural and functional behavior of the basic physics problems. The purpose of this review article is to present some of the recent methods for providing such series in closed form with applications to: (i) the summation of Kapteyn series for radiation from pulsars; (ii) the summation of other Kapteyn series in radiation problems; (iii) Kapteyn series arising in terahertz sideband spectra of quantum systems modulated by an alternating electromagnetic field; and (iv) some plasma problems involving sums of Bessel functions and their closed form summation using variations of the techniques developed for Kapteyn series. In addition, a short review is given of some other Kapteyn series to illustrate the ongoing deep interest and involvement of scientists in such problems and to provide further techniques for attempting to sum divers Kapteyn series.

MODELING NON-LINEAR COHERENT STATES IN FIBER ARRAYS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 349-355 ◽  
Author(s):  
R. DE J. LEÓN-MONTIEL ◽  
H. MOYA-CESSA
Keyword(s):  
Closed Form ◽  
Coherent States ◽  
Bessel Functions ◽  
Displacement Operator ◽  
Fiber Arrays ◽  
Non Linear ◽  
Phase Operators

A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.

On the Zeros of Derivatives of Bessel Functions

1988 ◽  
Vol 19 (6) ◽  
pp. 1450-1454 ◽  
Author(s):  
Lee Lorch ◽  
Peter Szego
Keyword(s):  
Bessel Functions ◽  
Derivatives Of ◽  
Zeros Of Derivatives

scholarly journals Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications

2021 ◽  
Vol 7 (3) ◽  
pp. 3418-3439
Author(s):  
Jamshed Nasir ◽  
◽  
Shahid Qaisar ◽  
Saad Ihsan Butt ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Operator ◽  
Real Numbers ◽  
Hadamard Inequality ◽  
Special Means ◽  
Special Cases ◽  
Derivatives Of ◽  
Quasi Convexity

<abstract><p>Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.</p></abstract>

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