Next Article in Journal
Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators
Next Article in Special Issue
Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses
Previous Article in Journal
The Constrained Median: A Way to Incorporate Side Information in the Assessment of Food Samples
Previous Article in Special Issue
Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients
Open AccessArticle

Limiting Values and Functional and Difference Equations

by N.-L. Wang 1,2, Praveen Agarwal 3,4,5,6,* and S. Kanemitsu 2,7
1
College of Applied Mathematics and Computer Science, Shangluo University, Shangluo 726000, Shaanxi, China
2
Institute of Sanmenxia Suda Transportation Energy Saving Technology, Sanmenxia 472000, Henan, China
3
International Center for Basic and Applied Sciences, Jaipur 302029, India
4
Anand International College of Engineering, Near Kanota, Agra Road, Jaipur 303012, Rajasthan, India
5
Harish-Chandra Research Institute (HRI), Jhusi, Uttar Pradesh 211019, India
6
Netaji Subhas University of Technology, Dwarka, New Delhi 110078, India
7
Faculty of Engrg, Kyushu Inst. Tech., 1-1 Sensuicho Tobata, Kitakyushu 804-8555, Japan
*
Author to whom correspondence should be addressed.
Dedicated to Professor Dr. Yumiko Hironaka with great respect and friendship.
Mathematics 2020, 8(3), 407; https://doi.org/10.3390/math8030407
Received: 16 February 2020 / Revised: 3 March 2020 / Accepted: 6 March 2020 / Published: 12 March 2020
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications)
Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. As main results, this involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We establish these by the relation between bases of the Kubert space of functions. Then these expressions are equated with other expressions in terms of special functions introduced by some difference equations, giving rise to analogues of the Lerch-Chowla-Selberg formula. We also state Abelian results which not only yield asymptotic formulas for weighted summatory function from that for the original summatory function but assures the existence of the limit expression for Laurent coefficients. View Full-Text
Keywords: Lerch-Chowla-Selberg formula; modular relation; Laurent coefficients; Lerch zeta-function; Hurwitz zeta-function Lerch-Chowla-Selberg formula; modular relation; Laurent coefficients; Lerch zeta-function; Hurwitz zeta-function
MDPI and ACS Style

Wang, N.-L.; Agarwal, P.; Kanemitsu, S. Limiting Values and Functional and Difference Equations. Mathematics 2020, 8, 407.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop