query: Holomorphic function such that $\theta\left(z+\omega_j\right)=a_j\theta\left(z\right)$ satisfies $\theta\left(z\right)=ae^{bz}$.
positive_passages.docid: 155531
positive_passages.text: Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
negative_passages.docid: 106971
negative_passages.text: Let $f:U \to V$ be a bijective holomorphic function. Show that inverse of $f$ is also holomorphic.
negative_passages.docid: 149328
negative_passages.text: A function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$ satisfies $f(z)+f(-z)=0$.(MADHAVA-2020)
negative_passages.docid: 82079
negative_passages.text: Holomorphic function satisfying $f^{-1}(\Bbb R)=\Bbb R$ is of the form $f(z)=az+b$
negative_passages.docid: 65753
negative_passages.text: The Function $f:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ defined by $f(r,\theta)=(r\cos\theta,r\sin\theta)$
negative_passages.docid: 129778
negative_passages.text: Primitive of holomorphic Function $\frac{1}{z}$ on an Annulus.
negative_passages.docid: 128547
negative_passages.text: $f:\mathbb C\rightarrow \mathbb C$ be an arbitrary analytic function satisfying $f(0)=0$ and $f(1)=2.$
negative_passages.docid: 94680
negative_passages.text: Holomorphic function $f$ such that $f'(z_0) \neq 0$
negative_passages.docid: 107968
negative_passages.text: holomorphic function on punctured disk satisfying $\left|f\left(\frac{1}{n}\right)\right|\leq\frac{1}{n!}$ has an essential singularity at $0$
negative_passages.docid: 141115
negative_passages.text: $f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$
negative_passages.docid: 56143
negative_passages.text: Proof of a basic $AC_\omega$ equivalence
negative_passages.docid: 27251
negative_passages.text: Holomorphic function with $f\circ f=f$
negative_passages.docid: 131999
negative_passages.text: Can a holomorphic function satisfy $f(1/n)=1/(n+1)$?
negative_passages.docid: 4698
negative_passages.text: Gamma Function Holomorphic
negative_passages.docid: 27344
negative_passages.text: Showing connection of cross-ratio and Schwarzian derivative for a holomorphic function $f$.
negative_passages.docid: 43136
negative_passages.text: Branch of the n-th root of a holomorphic function is holomorphic
negative_passages.docid: 12525
negative_passages.text: complex conjugates of holomorphic functions