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where are called the th generalized -Bernoulli polynomials of order attaches to.
In the special case,, the sequence are called the th generalized -Bernoulli numbers of order attaches to.
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Now we define the twisted generalized Euler polynomials of order attached to as follows: (2.5).
In the special case, are called the th -Euler numbers of order attached to.
Then, are called the th generalized -Euler polynomials of order attached to.
In the special case, are called the th generalized -Genocchi numbers of order attached to.
For, let us consider the twisted -extension of the generalized Euler numbers and polynomials of order attached to.
In [4, 7, 10 12], the generalized twisted Bernoulli polynomials of order attached to are also defined as follows: (1.6).
We give a new construction of the -Euler numbers and polynomials of higher order attached to Dirichlet's character.
For, let us consider the -extension of the generalized Genocchi polynomials of order attached to as follows: (21).
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