A New Type of Euler Polynomials and Numbers
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By defining two specific exponential generating functions, we introduce a kind of Euler polynomials and study its basic properties in detail. As an application of the introduced polynomials, we use them in computing some new series of Taylor type that contain the associated Euler numbers \(E_n(0)\) where \(E_n(x)\) is the Euler polynomial.
KeywordsEuler numbers and polynomials Appell polynomials binomial convolution exponential generating functions
Mathematics Subject Classification11B68 11C08 11Y35