Elliptic integrals, Jacobi's elliptic functions and Theta function.

The Matlab script implementations of Elliptic integrals of three types, Jacobi's elliptic functions and Jacobi theta functions of four types.

The main GOAL of the project is to provide the natural Matlab scripts WITHOUT external library calls like Maple and others. All scripts are developed to accept tensors as arguments and almost all of them have their complex versions. Performance and complete control on the execution are the main features.

Contents of the package

• Elliptic Functions
• ELLIPJ: Jacobi's elliptic functions
• ELLIPJI: Jacobi's elliptic functions of the complex argument
• JACOBITHETAETA: Jacobi's Theta and Eta Functions
• THETA: Theta Functions of Four Types
• Elliptic Integrals
• ELLIPTIC12: Incomplete Elliptic Integrals of the First, Second Kind and Jacobi's Zeta Function
• ELLIPTIC12I: Incomplete Elliptic Integrals of the First, Second Kind and Jacobi's Zeta Function of the complex argument
• ELLIPTIC3: Incomplete Elliptic Integral of the Third Kind
• ELLIPTIC123: Complete and Incomplete Elliptic Integrals of the First, Second, and Third Kind
• NEW! INVERSELLIPTIC2: INVERSE Incomplete Elliptic Integrals of the Second Kind

• Weierstrass's elliptic functions (in development)
• Elliptic Related Functions
• AGM: Artihmetic Geometric Mean
• NOMEQ: The Value of Nome q = q(m)
• INVERSENOMEQ: The Value of Nome m = m(q)
• References