Revision #778 → #1183 · back to history
addedElliptic integral (classical)d264cf77072b
addedElliptic integral (modern)f0e2c84e8b21
addedReduction to Legendre canonical formsf820560de39e
addedIncomplete elliptic integral of the first kind79b1ccb89994
addedJacobi's algebraic form of Fbd8d13807ea9
addedF as inverse of snd47ae3ada462
addedAddition theorem for Ff334837a0f2f
addedModulus transformation for F906daf829262
addedIncomplete elliptic integral of the second kind720d14ce3a3c
addedJacobi's algebraic form of Ea9a27b3f405c
addedMeridian arc length via E88279c4de489
addedAddition theorem for Ec0d2170121c7
addedModulus transformation for E277511f95f0a
addedIncomplete elliptic integral of the third kindec2a3ea4410b
addedCharacteristic n of Π3a16a38edb94
addedMeridian arc length via Π07703bc9caec
addedComplete elliptic integral of the first kind13d6e7a4ff11
addedPower series for K2e0da275dc72
addedK via Gauss hypergeometric functionfe8f4c09addc
addedK via arithmetic-geometric meanf42feffb5433
addedModulus transformation for K3a06a74b10f1
addedK closed form via gamma function81017eefc138
addedGamma closed form at r=2,3,702098f748017
addedSufficient imaginary quadratic field condition7848bebd3416
addedAsymptotic expression for K5ed3f26681b6
addedDifferential equation for K7fa2fe57d229
addedSecond solution of K differential equation16db845c822d
addedContinued fraction expansion of K9fcac77f3d69
addedInverting the period ratio via modular lambda02a7b490fe15
addedError analysis for period ratio inversion314c2ecb0cd0
addedComplete elliptic integral of the second kind96cc6b074c73
addedEllipse circumference via Ebbf2a71baa14
addedPower series for complete Ebfa1c2eb447c
addedComplete E via Gauss hypergeometric functiona964a87640fa
addedModulus transformation for complete Ebf96c7d459e8
addedAGM computation of complete E62bb7c2a450c
addedQuadratic convergence of AGM for Ef8b885c24dd7
addedE closed form via gamma functiondd2c0d992acb
addedSecond solution for E differential equation0aa19dcf658d
addedComplete elliptic integral of the third kindd1e36a76b587
addedAlternative sign convention for Πa25496db108d
addedJacobi zeta function23d1d35ca5e3
addedLegendre's relation (Pythagorean counterparts)1cccfda23774
addedLegendre's relation (tangential counterparts)ceeb7d2d4225
addedLemniscatic case of Legendre's identity15f72b6c4d39