O'Reilly logo

Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 25ELLIPTIC FUNCTIONS

‘Double, double, toil and trouble.’

SHAKESPEARE, Macbeth

25·01. Definition: illustrations.

The elliptic functions are characterized by the following properties. (1) They are single-valued analytic functions over the whole plane, except at isolated points where they have poles. (2) Two numbers ω and ω′, exist, whose ratio is not real, such that for all values of z

image

and therefore

image

for all positive and negative integral values of m and n.

    The name ‘elliptic function’ arose first from the relation of the functions to ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required