query: Entire functions satisfying a given condition
positive_passages.docid: 157844
positive_passages.text: If $f: \mathbb{C} \to \mathbb{C}$ is analytic and not linear, then $z, f(z), f(f(z)), \dots$ are linearly independent functions over $\mathbb{C}.$
negative_passages.docid: 114826
negative_passages.text: Zero Partials imply Constant Function Theorem or Proof
negative_passages.docid: 122356
negative_passages.text: Complex Analysis, Entire functions
negative_passages.docid: 98399
negative_passages.text: Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
negative_passages.docid: 91304
negative_passages.text: An entire function whose integral is bounded is identically zero
negative_passages.docid: 86473
negative_passages.text: Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
negative_passages.docid: 8179
negative_passages.text: If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
negative_passages.docid: 51934
negative_passages.text: Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
negative_passages.docid: 74392
negative_passages.text: Show that a function satisfies the Cauchy-Riemann function if and only if $\frac{df}{d\overline{z}}=0$
negative_passages.docid: 33099
negative_passages.text: If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial
negative_passages.docid: 49769
negative_passages.text: A function for which one-sided limits are zero and infinity
negative_passages.docid: 24810
negative_passages.text: Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
negative_passages.docid: 108997
negative_passages.text: Continuous functions that attain local extrema at every point
negative_passages.docid: 42358
negative_passages.text: Find a Borel subset satisfying the condition
negative_passages.docid: 14975
negative_passages.text: Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
negative_passages.docid: 10253
negative_passages.text: Proving that all entire & injective functions take the form $f = ax + b$?
negative_passages.docid: 97371
negative_passages.text: Proving a function is constant, under certain conditions?