## The Elliptic Functions as They Should be: An Account, with Applications, of the Functions in a New Canonical Form |

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### Contents

Symbols and Notation | xix |

Twenty Elliptic Functions and Their Forty Trig Series 1 | xxix |

Derivatives and Squares of the Elliptic Functions | 35 |

11 other sections not shown

### Common terms and phrases

addition theorem Appendix XI axis becomes binomial coefficients centre Chapter circle Cn2z coefficients cone CONFORMAL REPRESENTATION constant curve definite integrals denominator denote derivatives diagram differential distance Dn2z doubly periodic function dzjdw Elastica electrode ELLIPTIC FUNCTIONS equation example expression factor formulae four given gives Hence hyperbolic functions imaginary Incomplete Elliptic Integral infinite infinity integrand interesting Jacobian functions Jf functions length Liouville's theorem multiplied numerical obtained obviously origin period plane poles polygon powers problem radius rectangle relation result side Similarly simple sin2 sinty Sn*z Sn2a Sn2z solid angle square stream lines Table Theta functions trig integrals turn unity vertical Weierstrass's Weierstrass's elliptic function width wire write zero