Sentence examples for be a complex polynomial from inspiring English sources

Let be a complex polynomial sequence with.

Let f (x) be a complex polynomial and γbe one of its zeros.

Let (nin{mathbb{N}}), and let (q(x)=sum_{k=0}^{n}alpha_{k}x^{k}) be a complex polynomial.

Let (f z)) be a transcendental meromorphic function and (p z)=p_{k}z^{k}+p_{k-1}z^{k-1}+cdots+p_{1}z+p_{0}) be a complex polynomial of degree (k>0).

Let f ( z ) be a transcendental meromorphic function and p ( z ) = p k z k + p k − 1 z k − 1 + ⋯ + p 1 z + p 0 be a complex polynomial of degree k > 0. For given 0 < δ < | p k |, let λ = | p k | + δ, μ = | p k | − δ, then for given ε > 0 and for r large enough, ( 1 − ε ) T ( μ r k, f ) ≤ T ( r, f ∘ p ) ≤ ( 1 + ε ) T ( λ r k, f ).

Let f ( z ) be a transcendental meromorphic function, and let p ( z ) = p k z k + p k − 1 z k − 1 + ⋯ + p 1 z + p 0 be a complex polynomial of degree k > 0. For given 0 < δ < | p k |, let λ = | p k | + δ, μ = | p k | − δ, then for given ε > 0 and for sufficiently large r, ( 1 − ε ) T ( μ r k, f ) ≤ T ( r, f ∘ p ) ≤ ( 1 + ε ) T ( λ r k, f ).

Then there is a complex polynomial q of order n such that (p=alpha_{2n}qq_).

Theorem 1.4 Let k be a positive integer, b (≠0) be a complex number, h ( z ) be a polynomial, and let H ( f, f ′, …, f ( k ) ) be a differential polynomial with Γ γ | H < k + 1.

We obtain two results: Let k be a positive integer, b (≠0) be a complex number, and h ( z ) be a polynomial with degree at least 2, and H ( f, f ′, …, f ( k ) ) be a differential polynomial with Γ γ | H < k + 1.

Moreover, every linear operator acting on F ( C d ) can be written as a complex polynomial in the creation and annihilation operators.

For convenience, if p is a real (complex) polynomial, then we denote by (p_) the polynomial with the same principal coefficient and opposite roots.