analytic-functions

Name: analytic-functions
Availability: InStock
Author: parcadei

Verify analyticity via Cauchy-Riemann equations and compute power series expansions.

3.9k|296|Updated Dec 23, 2025

Search Tags:#mathematics #complex analysis #sympy #analytic functions #cauchy-riemann #power series

Ready to run

npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill analytic-functions-parcadei

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: analytic-functions
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/complex-analysis/analytic-functions
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill analytic-functions-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires sympy, z3-solver, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides strategies and tools for solving problems related to analytic functions in complex analysis, ensuring accurate mathematical computations and theoretical understanding.

Core Features & Use Cases

Cauchy-Riemann Equations: Verify if a function is analytic by checking these fundamental equations.
Power Series Expansion: Determine the series representation and radius of convergence for analytic functions.
Analytic Continuation: Understand methods to extend the domain of analytic functions.
Use Case: When faced with a complex function, use this skill to determine if it's analytic at a given point and to find its power series expansion.

Quick Start

Use the analytic-functions skill to check if f(z) = exp(z) is analytic at z0=0.

Frequently Asked Questions about analytic-functions

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I verify if a complex function is analytic using the Cauchy-Riemann equations?▼

To verify analytic functions, you check the Cauchy-Riemann equations using symbolic computation. This skill automates validating these fundamental equations for a given complex function at a specific point to determine its analyticity.

How do I find the power series expansion and radius of convergence for a complex function?▼

Finding the power series expansion for analytic functions involves determining their series representation and radius of convergence. This skill computes the series expansion for complex functions to support advanced calculus and theoretical physics problem-solving.

Can I use SymPy and Z3 for complex analysis computations and theorem proving?▼

Yes, you can use SymPy and Z3 for complex analysis computations and theorem proving. This skill requires SymPy for symbolic computation of analytic functions and the Z3-solver for mathematical verification of properties like analytic continuation.

What is analytic continuation and how does it extend the domain of analytic functions?▼

Analytic continuation is a mathematical method to extend the domain of analytic functions beyond their initial region of definition. This skill provides strategies to understand and apply analytic continuation methods for complex analysis problems.

What is the best way to solve complex analysis problems involving analytic functions programmatically?▼

The best way to solve complex analysis problems involving analytic functions is using symbolic computation and theorem provers. This skill provides methods to verify analyticity, compute power series, and perform analytic continuation using SymPy and Z3.

Does this approach to analytic functions work for advanced calculus and theoretical physics applications?▼

Yes, this approach to analytic functions works for advanced calculus and theoretical physics applications. The skill supports mathematical problem-solving in these domains by verifying Cauchy-Riemann equations and computing power series expansions for complex functions.