222 A. Mukliopadhyay — Elliptic Functions and Mean Values. [No 

 aad since for 



wo have also 



n = -(a^-cVEi 



and r 0 1 =0, 



since the elliptic integrals F and E are taken betweon 0 and i);. 

 Now 



-5 



SttP -1^ = ^ 3i(a2 -&2)^ /-j n sin ^ 



J 8 1^ a^cos^^ + i^siu^^j/' ^ 



re have 



Similarly, we have 



'•A=5 



" ). do. 



= -5 "sin - I T 



'^-JA=a "JA=a A(A2-c2}'^ 



3c(a2 — i^) Q sin 1^ cos ^ d^ 



^ Jo (a2cosH + i^sin2t)(a2cosH + i^«ii^'J'-c^)' 



