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**Identities of symmetry for generalized Euler polynomials.**
*(English)*
Zbl 1262.11022

Summary: We derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the \(p\)-adic fermionic integral expression of the generating function for the generalized Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized power sums.

### MSC:

11B68 | Bernoulli and Euler numbers and polynomials |

11B65 | Binomial coefficients; factorials; \(q\)-identities |

11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |

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\textit{D. S. Kim}, Int. J. Comb. 2011, Article ID 432738, 12 p. (2011; Zbl 1262.11022)

### References:

[1] | N. Koblitz, “A new proof of certain formulas for p-adic L-functions,” Duke Mathematical Journal, vol. 46, no. 2, pp. 455-468, 1979. · Zbl 0409.12028 |

[2] | E. Y. Deeba and D. M. Rodriguez, “Stirling’s series and Bernoulli numbers,” The American Mathematical Monthly, vol. 98, no. 5, pp. 423-426, 1991. · Zbl 0743.11012 |

[3] | F. T. Howard, “Applications of a recurrence for the Bernoulli numbers,” Journal of Number Theory, vol. 52, no. 1, pp. 157-172, 1995. · Zbl 0844.11019 |

[4] | T. Kim, “Symmetry p-adic invariant integral on \Bbb Zp for Bernoulli and Euler polynomials,” Journal of Difference Equations and Applications, vol. 14, no. 12, pp. 1267-1277, 2008. · Zbl 1229.11152 |

[5] | H. J. H. Tuenter, “A symmetry of power sum polynomials and Bernoulli numbers,” The American Mathematical Monthly, vol. 108, no. 3, pp. 258-261, 2001. · Zbl 0983.11008 |

[6] | S.-l. Yang, “An identity of symmetry for the Bernoulli polynomials,” Discrete Mathematics, vol. 308, no. 4, pp. 550-554, 2008. · Zbl 1133.11015 |

[7] | D. S. Kim and K. H. Park, “Identities of symmetry for Bernoulli polynomials arising from quotients of Volkenborn integrals invariant under S3,” submitted. · Zbl 1283.11040 |

[8] | D. S. Kim, “Identities of symmetry for generalized Bernoulli polynomials,” submitted. · Zbl 1205.33026 |

[9] | D. S. Kim and K. H. Park, “Identities of symmetry for Euler polynomials arising from quotients of fermionic integrals invariant under S3,” Journal of Inequalities and Applications, Article ID 851521, 16 pages, 2010. · Zbl 1191.81221 |

[10] | T. Kim, “A note on the generalized Euler numbers and polynomials,” http://arxiv.org/abs/0907.4889. |

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