lommel function
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2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
S. Chandak ◽  
S. K. Q. Al-Omari ◽  
D. L. Suthar

Abstract In this paper, we present two new unified integral formulas involving a generalized V-function. Some interesting special cases of the main results are also considered in the form of corollaries. Due to the general nature of the V-function, several results involving different special functions such as the exponential function, the Mittag-Leffler function, the Lommel function, the Struve function, the Wright generalized Bessel function, the Bessel function and the generalized hypergeometric function are obtained by specializing the parameters in the presented formulas. More results are also discussed in detail.


Author(s):  
Atul Dixit ◽  
Rahul Kumar

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.


2019 ◽  
Vol 75 (1) ◽  
Author(s):  
Robert E. Gaunt

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.


2015 ◽  
Vol 26 (7) ◽  
pp. 550-566 ◽  
Author(s):  
F. Bouzeffour ◽  
N. Chorfi
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