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In this paper, we study the ordinary differential equations associated with the generating function of general modified degenerate Euler numbers.

where and Then, one has the generating function of generalized Carlitz type -Euler polynomials attached to (2.31).

Thus, the generating function of the generalized -Bernoulli numbers attached to are as follows, (2.19).

The generating function of the generalized -Genocchi numbers attached to is given by (4.7).

Now we will deduce the generating function of the generalized q-Bessel function J n ( x, a ; q ).

We will have the generating function of -Genocchi polynomials and the generalized twisted -Genocchi numbers attached to.

In [21], Simsek defined generating function of by (2.25).

Let be the generating function of as follows: (2.14).

We have the generating function of -Genocchi polynomials.

Kim defined generating function of as follows [12]: (2.24).

Hence, we obtain the generating function of P n, d, N. □.