Series representations

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(n^1/2)+Pi u<xu+1/2)/;u ∈ Z

For m<1<n,Pi(u+1/2)<xu+1)-csc^-1(n^1/2)/;u ∈ Z

For n<1<m,csc^-1(m^1/2)+Pi u<xu+1/2)/;u ∈ Z

For n<1<m,Pi(u+1/2)<xu+1)-csc^-1(m^1/2)/;u ∈ Z

For 1<n< m,csc^-1(m^1/2)+Pi u<xu+1/2)/;u ∈ Z

For 1<n< m,Pi(u+1/2)<xu+1)-csc^-1(m^1/2)/;u ∈ Z

For 1<m< n,csc^-1(n^1/2)+Pi u<xu+1/2)/;u ∈ Z

For 1<m< n,Pi(u+1/2)<xu+1)-csc^-1(n^1/2)/;u ∈ Z

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(m^1/2)+Pi u/;u ∈ Z

Expansions at z==-csc^-1(m^1/2)+Pi u/;u ∈ Z

Expansions at z==csc^-1(n^1/2)+Pi u/;u ∈ Z

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

Other series representations

Expansions EllipticPi(n;sin^-1(z)|m) at z==infinity

Other expansions