Sentence examples for generated function of from inspiring English sources

If k is such that (k a,b =a-b) we simply write (F_{m}) (the generated function of m).

We define the geometric object R as a body of revolution generated by the function f(x) (or by the domain D), and call the function f(x) as the generated function of R and D as the generated domain of R. If the generated domain of R is a rectangle and a diamond, R is called a cylinder and a bicone, respectively.

In particular, if (k a,b =a-b) i.e. (q=1), (1/q^=0) and (F_{m}) denotes the generated function of m, then the binary map: (r_{m}(a,b)=aF_{m}(sqrt{a/b})) for all (a,b>0), (aneq b), defines a homogeneous mean with (r_{m}^{sigma}=m).

A regular mean m will be called σ-regular if the map (xlongmapsto m x,1)) is continuously differentiable on ((0,infty)) and the function (f_{m}) (called the generated function of m) defined by f_{m}(x)=frac{d}{dx} biggl(frac{x-1}{m x,1)} biggr) frac{x-1}{m x,1with (f_{m}(1)=1), satisfies the doubiggrnequality min bigl(1,1/x^{2} bigr)leq form}(x)leqmallbigl(1,1/x>02} bigr) for all (x>0).

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 ).

In Section 4, we define zeta functions related to -Genocchi polynomials and we have the generating function of the generalized -Genocchi numbers attached to.

Finally, we define zeta functions related to -Genocchi polynomials and have the generating function of the generalized -Genocchi numbers attached to.