query: $f(z) = xy + iy$ is nowhere analytic?
positive_passages.docid: 25633
positive_passages.text: Is the function $f(z)=xy+iy$ analytic?
negative_passages.docid: 65619
negative_passages.text: Does $f^{(n)} = 0$ imply that complex $f$ is a polynomial?
negative_passages.docid: 108792
negative_passages.text: Is the product of two non-holomorphic function always non-holomorphic?
negative_passages.docid: 65414
negative_passages.text: One-one analytic functions on unit disc
negative_passages.docid: 34060
negative_passages.text: Laurent Series of $f(z) = \sin {\frac{1}{z}}$ at $z=0$
negative_passages.docid: 141254
negative_passages.text: Zeros of analytic function of several real variables
negative_passages.docid: 58675
negative_passages.text: The real or purely imaginary solutions of the equation, $z^3+iz-1=0$ are?
negative_passages.docid: 3349
negative_passages.text: For $f$ an analytic function, what is
negative_passages.docid: 138329
negative_passages.text: Complex Analysis analytic function problem
negative_passages.docid: 130322
negative_passages.text: Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
negative_passages.docid: 128524
negative_passages.text: Proving there is no analytic function
negative_passages.docid: 141863
negative_passages.text: If the imaginary part of an entire function is never zero, the function is constant
negative_passages.docid: 40041
negative_passages.text: Proof of Non-Ordering of Complex Field
negative_passages.docid: 92537
negative_passages.text: Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots
negative_passages.docid: 96547
negative_passages.text: Is $|z|^2$ complex differentiable?
negative_passages.docid: 51577
negative_passages.text: Non-existence of a bijective analytic function between annulus and punctured disk
negative_passages.docid: 15175
negative_passages.text: When does a Möbius transformation map $\Im(z)>0$ to itself?