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Inverse Difference Operator and their Applications to Shifted Extorial and Exponential Functions.

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Title: Inverse Difference Operator and their Applications to Shifted Extorial and Exponential Functions.
Authors: M., Jenitha Borges1 jenithaborges@gmail.com, S., John Borg2 sjborg@gmail.com, G., Britto Antony Xavier3 brittoshc@gmail.com
Source: IAENG International Journal of Applied Mathematics. May2026, Vol. 56 Issue 5, p1887-1895. 9p.
Subjects: Nonlinear difference equations, Exponential functions, Data visualization, Addition (Mathematics), Special functions, Factorials
Abstract: This paper introduces a generalized form of the Extorial and Exponential functions with a shift parameter. Based on these definitions, a generalized inverse difference operator acting on Extorial and Exponential functions is formulated to study discrete integration of nonlinear expressions involving falling factorials. Several summation identities are derived through established lemmas and rigorous proofs. Illustrative examples are presented to demonstrate the applicability of the obtained results. Furthermore, graphical analysis is carried out to examine the behavior of the Extorial and Exponential functions under the inverse difference operator. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Inverse Difference Operator and their Applications to Shifted Extorial and Exponential Functions.
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  Data: <searchLink fieldCode="AR" term="%22M%2E%2C+Jenitha+Borges%22">M., Jenitha Borges</searchLink><relatesTo>1</relatesTo><i> jenithaborges@gmail.com</i><br /><searchLink fieldCode="AR" term="%22S%2E%2C+John+Borg%22">S., John Borg</searchLink><relatesTo>2</relatesTo><i> sjborg@gmail.com</i><br /><searchLink fieldCode="AR" term="%22G%2E%2C+Britto+Antony+Xavier%22">G., Britto Antony Xavier</searchLink><relatesTo>3</relatesTo><i> brittoshc@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. May2026, Vol. 56 Issue 5, p1887-1895. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+difference+equations%22">Nonlinear difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+functions%22">Exponential functions</searchLink><br /><searchLink fieldCode="DE" term="%22Data+visualization%22">Data visualization</searchLink><br /><searchLink fieldCode="DE" term="%22Addition+%28Mathematics%29%22">Addition (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Special+functions%22">Special functions</searchLink><br /><searchLink fieldCode="DE" term="%22Factorials%22">Factorials</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper introduces a generalized form of the Extorial and Exponential functions with a shift parameter. Based on these definitions, a generalized inverse difference operator acting on Extorial and Exponential functions is formulated to study discrete integration of nonlinear expressions involving falling factorials. Several summation identities are derived through established lemmas and rigorous proofs. Illustrative examples are presented to demonstrate the applicability of the obtained results. Furthermore, graphical analysis is carried out to examine the behavior of the Extorial and Exponential functions under the inverse difference operator. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 9
        StartPage: 1887
    Subjects:
      – SubjectFull: Nonlinear difference equations
        Type: general
      – SubjectFull: Exponential functions
        Type: general
      – SubjectFull: Data visualization
        Type: general
      – SubjectFull: Addition (Mathematics)
        Type: general
      – SubjectFull: Special functions
        Type: general
      – SubjectFull: Factorials
        Type: general
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      – TitleFull: Inverse Difference Operator and their Applications to Shifted Extorial and Exponential Functions.
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              M: 05
              Text: May2026
              Type: published
              Y: 2026
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