Sentence examples for function of the infinite order from inspiring English sources

In 2012, Kong [12] investigated the growth of the Laplace-Stieltjes transforms convergent in the right half-plane by using a type function of the infinite order.

Chuang [16, 17] investigated the existence of Borel directions of the meromorphic function of infinite order.

In order to describe the infinite order of fast growing entire functions precisely, we recall some definitions of entire functions of finite iterated order (e.g., see [3 8]).

The object of this section is to give the definition of some function spaces of infinite order, and the chains of the constructed spaces which will be used later; see Dubinskii [15, 16].

The sinh-mapping transforms a simple function like exp -z2) into an exp -z2functintoof infinite order.

Let f be an entire function of infinite order, with the hyper-order (rho_{2}(f)

The accuracy of the infinite-order cutoff function is greater than that of the eighth-order cutoff function when the flow is very smooth.

Theorem 1.1 Let f be a transcendental meromorphic function of infinite order ρ ( r ) on the whole complex plane, arg z = θ ( 0 ≤ θ < 2 π ) be one Borel direction of ρ ( r ) order of the function f and Ω : = Ω for any ε ( 0 < ε < π ).

Lemma 2.7 Let f be a transcendental meromorphic function of infinite order ρ ( r ) on the whole complex plane, arg z = θ ( 0 ≤ θ < 2 π ) be one Borel direction of ρ ( r ) order of the function f and Ω : = Ω for any ε ( 0 < ε < π ).

Then every solution f of the differential equation f ′ − e P ( z ) f = 1 is an entire function of infinite order.

Let f ( z ) be an entire function of infinite order with σ 2 ( f ) = σ, and μ ( r ) be the central index of f ( z ).