Abstract:
Genocchi numbers Gn and Genocchi polynomials Gn(x) can be derived
respectively by the following exponential generating functions.
2t
et + 1 =
1X n
=0
Gntn
n!;
2tetx
et + 1 =
1X n
=0
Gn(x)tn
n!; (jtj < π)
In the usual notation, Bn(x) and En(x) are denoted by Bernoulli and
Euler polynomials of degree n in x, defined by the generating functions
respectively.
tetx
et − 1 =
1X n
=0
Bn(x)tn
n!; (jtj < 2π)
2etx
et + 1 =
1X n
=0
En(x)tn
n!; (jtj < π)
where Bn and En are respectively Bernoulli and Euler numbers.
In 2014, Araci et al. [3] established the Basic properties of Bernoulli
numbers and polynomials, Euler numbers and polynomials and Genocchi numbers and polynomials are discussed. In this thesis, we can
derive some identities relationship between the Genocchi polynomials
to Bernoulli and Euler polynomials and we get some applications for
Genocchi polynomials.
