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 EllipticPi

Generalized power series

Expansions at generic point n==n0

For the function itself

Expansions at n==0

Expansions at n==1

Expansions at n==infinity

Expansions at generic point z==z0

For the function itself

Expansions on branch cuts

Formulas on real axis for real m, n

For m<1<n,csc-1(n1/2)+Pi u<xu+1/2)/;uZ

For m<1<n,Pi(u+1/2)<xu+1)-csc-1(n1/2)/;uZ

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

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

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

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

For 1<m< n,csc-1(n1/2)+Pi u<xu+1/2)/;uZ

For 1<m< n,Pi(u+1/2)<xu+1)-csc-1(n1/2)/;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==csc-1(n1/2)+Pi u/;uZ

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