An Elementary Treatise on Elliptic Functions

1-k² sn² 1+ku 2siK A₁ addition-equation b₁ cn u dn coefficients complete functions constant cos² cx² denom denominator differential equation dn² dx² elliptic functions elliptic integrals equation becomes expression factor formula functions sn gives hence imaginary Jacobi's k² sin² k²² k²x² ksin M₁ modular equation modulus multiplying numerator observing obtain odd function parameter quadric quartic function rational function regards relation right-hand side satisfied second transformation similarly sin2 sin³ sin³µ sn² 4sw sn² a sn² sn³ sn³u substituting thence theorem theory u³v u³v² uv³ whence writing therein Θα аф пи