## Abstract

Eight basic identities of symmetry in three variables, which are related to degenerate Euler polynomials and alternating generalized falling factorial sums, are derived. These are the degenerate versions of the symmetric identities in three variables obtained in a previous paper. The derivations of identities are based on the *p*-adic integral expression of the generating function for the degenerate Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized falling factorial sums. Those eight basic identities and most of their corollaries are new, since there have been results only about identities of symmetry in two variables.

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## Acknowledgements

The first author is appointed as a chair professor at Tianjin Polytechnic University by Tianjin City in China from August 2015 to August 2019. The authors would like to express their sincere gratitude to referees for their valuable comments and information.

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Kim, T., Kim, D.S. Identities of Symmetry for Degenerate Euler Polynomials and Alternating Generalized Falling Factorial Sums.
*Iran J Sci Technol Trans Sci* **41**, 939–949 (2017). https://doi.org/10.1007/s40995-017-0326-6

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DOI: https://doi.org/10.1007/s40995-017-0326-6

### Keywords

- Degenerate Euler polynomial
- Alternating generalized falling factorial sum
- Fermionic
*p*-adic integral - Identities of symmetry