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New Generalization of Eulerian Polynomials and their Applications |
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PP: 59-63 |
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Author(s) |
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Serkan Araci,
Mehmet Acikgoz,
Erdoğan Şen,
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Abstract |
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| In the present paper, we introduce Eulerian polynomials with parameters a and b and give the definition of them. By using
the definition of generating function for our polynomials, we derive some new identities in Analytic Numbers Theory. Also, we give
relations between Eulerian polynomials with parameters a and b, Bernstein polynomials, Poly-logarithm functions, Bernoulli and Euler
numbers. Moreover, we see that our polynomials at a = −1 are related to Euler-Zeta function at negative inetegers. Finally, we get
Witt’s formula for new generalization of Eulerian polynomials which we express in this paper. |
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