query: Proving an analytic function is rational
positive_passages.docid: 21978
positive_passages.text: Meromorphic on unit disc with absolute value 1 on the circle is a rational function.
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 39021
negative_passages.text: Proving that $\sqrt{2}+\sqrt{3}$ is irrational
negative_passages.docid: 92029
negative_passages.text: Is this rational function convex?
negative_passages.docid: 62901
negative_passages.text: Bound for Analytic Function on Unit Disk
negative_passages.docid: 3349
negative_passages.text: For $f$ an analytic function, what is
negative_passages.docid: 151439
negative_passages.text: $\sqrt{1-x^2}$ is not a rational function
negative_passages.docid: 23752
negative_passages.text: Proving Irrationality
negative_passages.docid: 106290
negative_passages.text: Prove a function is constant. (complex analysis)
negative_passages.docid: 111233
negative_passages.text: Analytic function and the Lagrange interpolating polynomial
negative_passages.docid: 153043
negative_passages.text: Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
negative_passages.docid: 74051
negative_passages.text: No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
negative_passages.docid: 132478
negative_passages.text: Prove that continuous functions mapping irrationals to rationals must be constant
negative_passages.docid: 65901
negative_passages.text: Solution verification to complex analysis problem, prove $f$ is a polynomial.
negative_passages.docid: 93400
negative_passages.text: Prove that an analytic function with a constant imaginary part is constant itself
negative_passages.docid: 103328
negative_passages.text: Rational Roots of Riemann's $\zeta$ Function
negative_passages.docid: 106175
negative_passages.text: A function is analytic if and only if it is holomorphic