IO 



MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



, 

 cosh 



o 



Jl / (fr 



= + ^V3p sinh 



2 3 



y\ . / . , <t> 

 = - * v 3p sinh 

 2 ^ 3 



If p > o, q < o, ? 2 > f, 



yi = 2\/? cosh 

 3 



yi 



2 



If < o 



sinh 



sinh <f> = 



-P' 



If p > o, ? 2 < 



y\ = 2\/ p sinh 



y2 = H ^'x^ 3^ cosh 



\5 



y 3 2 3 cos ^ 



COS </) 



cos 



OTl y - , <f> 



+ V 3P sin 



O^ 



sin-- 



1.272 Biquadratic equations. 



<ZO# 4 + 



Substitute 



+ 2^ + W + ^4 = 



