LEGENDRES IDENTITY:

[Annotate][Shownotes]




A nice proof of this follows by
(i) differentiating both sides - one gets zero- and then
(ii) taking the limit at .
We illustrate this in

It is interesting to note that Legendres faith in and knowledge of limits precluded his developing this proof. Instead he evaluated all quantities at (the third <A HREF="">singular modulus</A>) a considerable tour de force!