In mathematics, the Carlson symmetric forms of elliptic integrals, R_C, R_D, R_F and R_J are defined by Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse and were first studied by Giulio Fagnano and Leonhard Euler. ...

Relations concerning to Legendre form of elliptic integrals

In mathematics, the Legendre forms of elliptic integrals, F(φ,k), E(φ,k) and P(φ,k,n) are defined by and Categories: Math stubs ... In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse and were first studied by Giulio Fagnano and Leonhard Euler. ...

Incomplete elliptic integrals

Incomplete elliptic integrals can be calculated easily using Carlson symmetric forms: In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse and were first studied by Giulio Fagnano and Leonhard Euler. ...

Complete elliptic integrals

Complete elliptic integrals can be calculated by substituting : In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse and were first studied by Giulio Fagnano and Leonhard Euler. ...

Other properties

Duplication theorem:

where .

Homogeneousity: