Subsections

• 5.3.1 Complete Elliptic Integrals
• 5.3.2 Incomplete Elliptic Integrals
• 5.3.3 Jacobi's Elliptic Functions
• 5.3.4 Weierstrass' Elliptic Functions
• 5.3.5 Articles

5.3 Elliptic Integrals and Functions

An important recent change in the old subject of elliptic integrals is a renormalization of the definitions of the integrals. This is due to B. C. Carlson: references will be found in §5.3.5.

5.3.1 Complete Elliptic Integrals

[Bel88], [Bul65a, Algol], [Bul65b, Algol], [Bul69b, Algol], [Cod65a], [Cod65b], [DR94a, Fortran], [Luk69b], [MH73, Algol]. Libraries: [Bak92], [Mos89], [ULI90], [WNO94], [ZJ96], IMSL, Numerical Recipes. Systems: Maple, Mathematica.

5.3.2 Incomplete Elliptic Integrals

[Bul65a, Algol], [Bul69b, Algol], [Car87, Fortran], [Car88, Fortran], [CN81, Fortran], [Luk69b], [PT90, Fortran]. Libraries: [Bak92], [Mos89], [Tho97], [ULI90], [ZJ96], IMSL, NAG, Numerical Recipes, SLATEC. Systems: Maple, Mathematica.

5.3.3 Jacobi's Elliptic Functions

This subsection includes the theta functions. [Bul65a, Algol]. Libraries: [Bak92], [Tho97], [Mos89], [ULI90], [ZJ96], IMSL, NAG, Numerical Recipes. Systems: Maple (includes inverse functions), Mathematica (includes inverse functions).

5.3.4 Weierstrass' Elliptic Functions

This subsection includes modular functions. [Eck76], [Eck77], [Eck80, Fortran]. Libraries: [Bak92], [ULI90], IMSL. Systems: Maple, Mathematica.

5.3.5 Articles

[ACJP85, includes survey], [Bul69a], [Car65], [Car77a], [Car77b], [Car79], [Car87], [Car88], [Car89], [Car91], [Car92], [Car95], [CGL90], [Cri89], [DR94b], [FGG82], [FI94], [FL67], [Kin88], [Lee90], [Lee92], [Luk68], [Luk69b], [Luk70b], [LY88], [MH73, Algol], [Mid75], [Mor99], [NC66], [PDK96], [Sal89], [War60].