scholarly journals A q-analogue of r-Whitney numbers of the second kind and its Hankel transform

2020 ◽  
Vol 21 (03) ◽  
pp. 258-272
Author(s):  
Roberto B. Corcino ◽  
Jay M. Ontolan ◽  
Jennifer Cañete ◽  
Mary Joy R. Latayada
Keyword(s):  
Hankel Transform ◽  
Whitney Numbers

Hankel Transform of the Type 2 (p,q)-Analogue of r-Dowling Numbers

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 343
Author(s):  
Roberto Corcino ◽  
Mary Ann Ritzell Vega ◽  
Amerah Dibagulun
Keyword(s):  
Hankel Transform ◽  
Convolution Type ◽  
Combinatorial Interpretation ◽  
Whitney Numbers

In this paper, type 2 (p,q)-analogues of the r-Whitney numbers of the second kind is defined and a combinatorial interpretation in the context of the A-tableaux is given. Moreover, some convolution-type identities, which are useful in deriving the Hankel transform of the type 2 (p,q)-analogue of the r-Whitney numbers of the second kind are obtained. Finally, the Hankel transform of the type 2 (p,q)-analogue of the r-Dowling numbers are established.

scholarly journals Hankel Transform of the First Form (q,r)-Dowling Numbers

2021 ◽  
Vol 14 (3) ◽  
pp. 746-759
Author(s):  
Roberto Bagsarsa Corcino
Keyword(s):  
Hankel Transform ◽  
Exponential Polynomial ◽  
Trans Form ◽  
Whitney Numbers ◽  
Special Case

In this paper, the Hankel transform of the generalized q-exponential polynomial of the first form (q, r)-Whitney numbers of the second kind is established using the method of Cigler. Consequently, the Hankel trans- form of the first form (q, r)-Dowling numbers is obtained as special case.

scholarly journals Hankel Transform of the Second Form (q,r)-Dowling Numbers

2019 ◽  
Vol 12 (4) ◽  
pp. 1676-1688
Author(s):  
Roberto Bagsarsa Corcino ◽  
Jay Ontolan ◽  
Gladys Jane Rama
Keyword(s):  
Hankel Transform ◽  
Whitney Numbers ◽  
Divisibility Property

In this paper, using the rational generating for the second form of the q-analogue of r-Whitney numbers of the second kind, certain divisibility property for this form is established. Moreover, the Hankel transform for the second form of the q-analogue of r-Dowling numbers is derived. 

scholarly journals The Translated Dowling Polynomials and Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mahid M. Mangontarum ◽  
Amila P. Macodi-Ringia ◽  
Normalah S. Abdulcarim
Keyword(s):  
Integral Representation ◽  
Explicit Formula ◽  
Generating Function ◽  
Generating Functions ◽  
Hankel Transform ◽  
Bell Polynomials ◽  
Basic Properties ◽  
Whitney Numbers ◽  
Exponential Generating Function

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.

scholarly journals Hankel Transform of (q,r)-Dowling Numbers

2019 ◽  
Vol 12 (2) ◽  
pp. 279-293
Author(s):  
Roberto B. Corcino ◽  
Mary Joy Regidor Latayada ◽  
Mary Ann Ritzell P. Vega
Keyword(s):  
Hankel Transform ◽  
Convolution Type ◽  
Combinatorial Interpretation ◽  
Whitney Numbers

In this paper, we establish certain combinatorial interpretation for $q$-analogue of $r$-Whitney numbers of the second kind defined by Corcino and Ca\~{n}ete in the context of $A$-tableaux. We derive convolution-type identities by making use of the combinatorics of $A$-tableaux. Finally, we define a $q$-analogue of $r$-Dowling numbers and obtain some necessary properties including its Hankel transform.

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

scholarly journals Interior-stress fields produced by a general axisymmetric punch

Friction ◽  
2021 ◽  
Author(s):  
Longxiang Yang ◽  
Zhanjiang Wang ◽  
Weiji Liu ◽  
Guocheng Zhang ◽  
Bei Peng
Keyword(s):  
Hankel Transform ◽  
Elastic Half Space ◽  
Stress Fields ◽  
Dual Integral Equations ◽  
Total Load ◽  
Interior Stress ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Relationship Of ◽  
Analytical Expressions

AbstractThis work is a supplement to the work of Sneddon on axisymmetric Boussinesq problem in 1965 in which the distributions of interior-stress fields are derived here for a punch with general profile. A novel set of mathematical procedures is introduced to process the basic elastic solutions (obtained by the method of Hankel transform, which was pioneered by Sneddon) and the solution of the dual integral equations. These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space. The usually known cases of punch profiles are reconsidered according to the general formulas derived in this study, and the deduced results are verified by comparing them with the classical results. Finally, these general formulas are also applied to evaluate the von Mises stresses for several new punch profiles.

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