<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function. Also, we present generalizations of some familiar identities and connection between these types of Bernoulli, Euler, and Genocchi polynomials. Moreover, we establish new analogues of the Euler identity for degenerate Bernoulli polynomials and numbers.</p></abstract>

We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function. Also, we present generalizations of some familiar identities and connection between these types of Bernoulli, Euler, and Genocchi polynomials. Moreover, we establish new analogues of the Euler identity for degenerate Bernoulli polynomials and numbers.

New degenerate Bernoulli, Euler, and Genocchi polynomials

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"New degenerate Bernoulli, Euler, and Genocchi polynomials"}

We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function....

New degenerate Bernoulli, Euler, and Genocchi polynomials

Published Online: Dec 24, 2020

Page range: 1 - 16

Received: Jan 26, 2019

Accepted: May 27, 2019

DOI: https://doi.org/10.1515/puma-2015-0037

Keywords
degenerate Bernoulli polynomials and numbers, degenerate Euler polynomials, degenerate Genocchi polynomials, Euler identity for Bernoulli numbers, Carlitz-Tsallis degenerate exponential function, umbral calculus

© 2020 Orli Herscovici et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

New degenerate Bernoulli, Euler, and Genocchi polynomials

Published Online: Dec 24, 2020

Page range: 1 - 16

Received: Jan 26, 2019

Accepted: May 27, 2019

DOI: https://doi.org/10.1515/puma-2015-0037

Keywordsdegenerate Bernoulli polynomials and numbers, degenerate Euler polynomials, degenerate Genocchi polynomials, Euler identity for Bernoulli numbers, Carlitz-Tsallis degenerate exponential function, umbral calculus

© 2020 Orli Herscovici et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
degenerate Bernoulli polynomials and numbers, degenerate Euler polynomials, degenerate Genocchi polynomials, Euler identity for Bernoulli numbers, Carlitz-Tsallis degenerate exponential function, umbral calculus