Sentence examples for be small functions of from inspiring English sources

Let and be small functions of and.

Let α be an entire function, (a_{n-1},ldots,a_{1},a_{0}), R be small functions of f, and let (ngeq2) be an integer.

Let α be an entire function, R and (a_{i}) ((i=0,1, ldots,n-1)) be small functions of f with (a_{0}notequiv0).

associated with f, where a j are small functions of f for j = 1, 2, …, k.

Suppose that (R z)), (p_{1} z)), (p_{2} z)) are small functions of f and (alpha _{1}), (alpha_{2}) are nonconstant polynomials.

For case 1, it is impossible as α is an entire function and R, (a_{1},ldots,a_{n}) are small functions of f.

possesses at most one admissible transcendental entire solution of finite order such that all coefficients of M ( z, f ) are small functions of f.

Then the differential equation (pff'-q=Rmathrm{e}^{alpha}) has no transcendental meromorphic solutions, where p, q, and R are small functions of f with (pqnot equiv0).

Then there exist no transcendental entire solutions f and g satisfying the equation a f n + b g m = 1, with a, b being small functions of f and g, respectively.

It is difficult to give the form of meromorphic solutions of the following differential equations: f^{n}f'+Q_{d} z,f =p_{1} z e^{alpha_{1} z)}+p_{2}(z)e^{alpha_{2}(z)}, (2) where (Q_{d} z,f)) is a differential polynomial in f with small functions of f as the coefficients, (p_{1}), (p_{2}) are small functions of f, (alpha_{1} z)), (alpha_{2} z)) are nonconstant polynomials.

The main purpose of this paper is to present some properties of the meromorphic solutions of complex difference equation of the form, where and are two finite index sets, are distinct, nonzero complex numbers, and are small functions relative to is a rational function in with coefficients which are small functions of.