Lemniscate elliptic functions: Difference between revisions

Revision as of 21:57, 28 September 2012

Revision as of 22:06, 28 September 2012

Line 27:

:<math>cl(r)=c</math>

:<math> r=\int_c^1\frac{dt}{\sqrt{1-t^4}}</math>

They are doubly periodic (or elliptic) functions in the complex plane, with periods 2Ω2π''G'' and 22π''i''Ω''G'', where [[Gauss's constant]] ''G'' is given by

:<math>\Omegapi G=2\int_0^1\frac{dt}{\sqrt{1-t^4}}</math>

is the length of one lobe of the lemniscate, and plays roughly the same role for the lemniscate functions that π plays for the trigonometric functions.

==See also==