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analytic-functions

Verify analyticity with Cauchy-Riemann equations and compute power series using Sympy.

8|1|Updated Jan 4, 2026
Search Tags:#z3#complex analysis#sympy#analytic functions#cauchy-riemann#power series
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill analytic-functions
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: analytic-functions
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/complex-analysis/analytic-functions
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill analytic-functions

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill 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, including verifying analyticity and performing analytic continuation.

Core Features & Use Cases

  • Cauchy-Riemann Equations: Verify if a function is analytic by checking the Cauchy-Riemann conditions.
  • Power Series Expansion: Compute and analyze the power series representation of analytic functions.
  • Analytic Continuation: Understand and apply techniques for extending analytic functions.
  • Use Case: When faced with a complex function, use this skill to determine if it's analytic at a specific point or within a region, and to explore its behavior through power series.

Quick Start

Use the analytic-functions skill to check if f(z) = u(x,y) + iv(x,y) satisfies the Cauchy-Riemann equations.

Frequently Asked Questions about analytic-functions

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

FAQPage Schema
How do I verify analyticity using the Cauchy-Riemann equations?▼

To verify analyticity, check if the function satisfies the Cauchy-Riemann equations using symbolic differentiation. This Skill applies Sympy to compute partial derivatives of u(x,y) and v(x,y) to confirm if the complex function is analytic at a specific point or region.

How do I compute the power series expansion of an analytic function?▼

Compute the power series expansion by applying Sympy for series computation. The Skill calculates the power series representation of analytic functions to help you explore their behavior and properties within a specific radius of convergence.

Can I use Z3 theorem proving for complex analysis problems?▼

Yes, you can use Z3 for theorem proving in complex analysis. The Skill utilizes Z3 to logically verify properties and solve problems related to analytic functions, complementing Sympy's symbolic differentiation capabilities for rigorous mathematical validation.

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

Analytic continuation is a technique to extend the domain of an analytic function beyond its initial region of definition. This Skill provides strategies to understand and apply these continuation techniques for complex analysis problem-solving.

Does this Skill require any external dependencies to run?▼

No external Skill dependencies are required to run this tool. It operates independently using internal scripts and references to execute Sympy for symbolic math operations and Z3 for theorem proving.

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