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 EllipticE

Series representations

Generalized power series

Expansions at generic point z==z0

For the function itself

Expansions on branch cuts

Formulas on real axis for real m

For m>1,csc-1(m1/2)+Pi u<xu+1/2)/;uZ

For m>1,Pi(u+1/2)<xu+1)-csc-1(m1/2)/;uZ

Formulas for vertical intervals

For Re(z0/2 Pi-1/4) ∈ Z

For Re(z0/2 Pi-3/4) ∈ Z

Expansions at z==0

Expansions at z==csc-1(m1/2)+Pi u/;uZ

Expansions at z==-csc-1(m1/2)+Pi u/;uZ

Expansions at z==Pi/2+2Pi u/;uZ && m>1

Expansions at z==3Pi/2+2Pi u/;uZ && m>1

Expansions at z==infinity

Expansions at generic point m==m0

For the function itself

Expansions at m==0

Expansions at m==1

Expansions at m==infinity

Expansions at m==infinity NEW E

Residue representations

Other series representations

Expansions E(sin-1(z)|m) at z==0

Expansions E(sin-1(z)|m) at z==infinity

Expansions E(sin-1(z)|m) at m==0

Expansions E(sin-1(z)|m) at m==1

Other expansions