query: is there an non-constant analytic complex function that receives only real values ?
positive_passages.docid: 146654
positive_passages.text: Real valued analytic function defined on a connected set is constant
negative_passages.docid: 138559
negative_passages.text: How can I show that $\frac{1}{1+|z|^2}$ isn't analytic at $z=1$?
negative_passages.docid: 149529
negative_passages.text: Name for complex number with nonzero imaginary component
negative_passages.docid: 15797
negative_passages.text: Holomorphic function having finitely many zeros in the open unit disc
negative_passages.docid: 96050
negative_passages.text: $f$ an analytic function on $\mathbb{C}$ which takes values in $\mathbb{C}\backslash(-\infty,0]$ implies constant
negative_passages.docid: 74339
negative_passages.text: Integrable function whose Fourier transform is not integrable
negative_passages.docid: 148474
negative_passages.text: on the boundary of analytic functions
negative_passages.docid: 140602
negative_passages.text: If the absolute value of an analytic function $f$ is a constant, must $f$ be a constant?
negative_passages.docid: 38674
negative_passages.text: Do complex numbers really exist?
negative_passages.docid: 9737
negative_passages.text: Complex number operations: telling Mathematica variables are real
negative_passages.docid: 116495
negative_passages.text: How to eliminate the zero real part of a purely imaginary number?
negative_passages.docid: 137971
negative_passages.text: Existence of an holomorphic function
negative_passages.docid: 136793
negative_passages.text: Does there exist a holomorphic function $\varphi(z)$ such that $\varphi^2(z) = \psi(z)$
negative_passages.docid: 148247
negative_passages.text: Prove the existence of an analytic function
negative_passages.docid: 3349
negative_passages.text: For $f$ an analytic function, what is
negative_passages.docid: 93888
negative_passages.text: What do we lose passing from the reals to the complex numbers?
negative_passages.docid: 22153
negative_passages.text: Power Series of a Holomorphic Function determined by its Real Part and $f(0)$?