analytic function

C24991

concept

An analytic function is a complex-valued function that is locally given by a convergent power series, meaning it is differentiable at every point in its domain and in a neighborhood around each point.

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All labels observed (14)

Label	Occurrences
complex analytic function	7
analytic function canonical	5
automorphic form	2
entire function	2
Blaschke product	1
bounded holomorphic function	1
complex-analytic function	1
complex-analytic functions	1
extremal function	1
holomorphic function	1
object of complex analysis	1
object of geometric function theory	1
rational inner function	1
univalent function	1

Description generation (CDg)

The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.

Instruction

generate a one-sentence description for a given conceptual class.
# Response Format
Return only the sentence: "Description: [one-sentence description of the conceptional class]"

Input

Class: analytic function

Generated description

An analytic function is a complex-valued function that is locally given by a convergent power series, meaning it is differentiable at every point in its domain and in a neighborhood around each point.

Instances (16)

Instance	Via concept surface
Hasse–Weil zeta function	—
Dirichlet L-functions	complex analytic function
L-functions surface form: L-function	complex analytic function
Gauss hypergeometric function	—
Jacobi theta functions	complex-analytic functions
modular j-invariant	complex analytic function
Riemann xi function	entire function
Blaschke products surface form: Blaschke product	—
Selberg zeta function	—
Barnes G-function	entire function
Siegel modular form	complex analytic function
Harish-Chandra c-function	—
Koebe function	holomorphic function
Artin L-functions	complex analytic function
Eisenstein series	complex analytic function
Hurwitz zeta function	complex analytic function