- Open Access
Some identities of Genocchi polynomials arising from Genocchi basis
© Kim et al.; licensee Springer 2013
- Received: 21 December 2012
- Accepted: 13 January 2013
- Published: 11 February 2013
In this paper, we give some interesting identities which are derived from the basis of Genocchi. From our methods which are treated in this paper, we can derive some new identities associated with Bernoulli and Euler polynomials.
- Vector Space
- Dimensional Vector
- Good Basis
- Natural Basis
- Euler Number
with the usual convention about replacing by .
with the usual convention about replacing by .
Let be the -dimensional vector space over ℚ. Probably, is the most natural basis for . But is also a good basis for the space for our purpose of arithmetical applications of Genocchi polynomials. Let . Then can be expressed by .
In this paper, we develop some new methods to obtain some new identities and properties of Genocchi polynomials which are derived from the Genocchi basis.
Therefore, by (10) and (18), we obtain the following theorem.
Theorem 1 For , let with .
Therefore, by (22), we obtain the following theorem.
Therefore, by (31) and (33), we obtain the following theorem.
Dedicated to Professor Hari M Srivastava.
The authors would like to express their gratitude for the valuable comments and suggestions of referees. This research was supported by Kwangwoon University in 2013.
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