scholarly journals Radii of k-starlikeness of order α of Struve and Lommel functions

2021 ◽  
Vol 22 (1) ◽  
pp. 5
Author(s):  
I. Aktas ◽  
E. Toklu ◽  
H. Orhan
Keyword(s):  
Lommel Functions

Asymptotic expansions and converging factors V. Lommel, Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions

1959 ◽  
Vol 249 (1257) ◽  
pp. 284-292 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Lommel Functions ◽  
Special Cases

A theory of Lommel functions is developed, based upon the methods described in the first four papers (I to IV) of this series for replacing the divergent parts of asymptotic expansions by easily calculable series involving one or other of the four ‘basic converging factors’ which were investigated and tabulated in I. This theory is then illustrated by application to the special cases of Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions.

scholarly journals Inequalities for Some Integrals Involving Modified Lommel Functions of the First Kind

2019 ◽  
Vol 75 (1) ◽  
Author(s):  
Robert E. Gaunt
Keyword(s):  
Hypergeometric Function ◽  
Generalized Hypergeometric Function ◽  
Double Inequality ◽  
Lommel Functions ◽  
Modified Struve Function ◽  
Lommel Function

AbstractIn this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $$t_{\mu ,\nu }(x)$$tμ,ν(x). In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality, involving the modified Lommel function $$t_{\mu ,\nu }(x)$$tμ,ν(x), for a generalized hypergeometric function. The inequalities obtained in this paper generalise recent bounds for integrals involving the modified Struve function of the first kind.

scholarly journals Tight focusing of light beams: a set of exact solutions

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160538 ◽  
Author(s):  
John Lekner
Keyword(s):  
Exact Solutions ◽  
Focal Plane ◽  
Bessel Functions ◽  
Momentum Conservation ◽  
Focal Region ◽  
Beam Direction ◽  
Lommel Functions ◽  
Tight Focusing ◽  
Causal Propagation ◽  
Light Beams

Exact solutions of Maxwell's equations representing light beams are explored. The solutions satisfy all of the physical requirements of causal propagation and of energy, momentum and angular momentum conservation. A set of solutions can be found from a proto-beam by an imaginary translation along the beam direction. The proto-beam is given analytically in terms of the Bessel functions J 0 , J 1 and the Lommel functions U 0 , U 1 , or equivalently in terms of products of the spherical Bessel functions and Legendre polynomials. The complex wavefunction has rings of zeros in the focal plane. Localization of the focal region is to within about one half of the vacuum wavelength.

Accurate efficient evaluation of Lommel functions for arbitrarily large arguments

Metrologia ◽  
2003 ◽  
Vol 40 (1) ◽  
pp. S5-S8 ◽  
Author(s):  
Eric L Shirley ◽  
Eric K Chang
Keyword(s):  
Lommel Functions

Lommel Functions of Two Imaginary Arguments

1966 ◽  
Vol 20 (96) ◽  
pp. 624
Author(s):  
Y. L. L. ◽  
E. Wai-Kwok Ng
Keyword(s):  
Lommel Functions

scholarly journals Partial sums of the normalized Lommel functions

2015 ◽  
pp. 1189-1199 ◽  
Author(s):  
Murat Çağlar ◽  
Erhan Deniz
Keyword(s):  
Partial Sums ◽  
Lommel Functions

scholarly journals Certain Geometric Properties of Lommel and Hyper-Bessel Functions

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 240
Author(s):  
Saima Mushtaq ◽  
Mohsan Raza ◽  
Muhey Din
Keyword(s):  
Bessel Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Geometric Properties ◽  
Lommel Functions

In this article, we are mainly interested in finding the sufficient conditions under which Lommel functions and hyper-Bessel functions are close-to-convex with respect to the certain starlike functions. Strongly starlikeness and convexity of Lommel functions and hyper-Bessel functions are also discussed. Some applications are also the part of our investigation.

scholarly journals On Hurwitz zeta function and Lommel functions

2020 ◽  
pp. 1-12
Author(s):  
Atul Dixit ◽  
Rahul Kumar
Keyword(s):  
Zeta Function ◽  
Infinite Series ◽  
Hurwitz Zeta Function ◽  
Type Transformation ◽  
Lommel Functions ◽  
Special Case ◽  
Lommel Function

We obtain a new proof of Hurwitz’s formula for the Hurwitz zeta function [Formula: see text] beginning with Hermite’s formula. The aim is to reveal a nice connection between [Formula: see text] and a special case of the Lommel function [Formula: see text]. This connection is used to rephrase a modular-type transformation involving infinite series of Hurwitz zeta function in terms of those involving Lommel functions.

Sign in / Sign up

Export Citation Format

Share Document