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(m^1/2)+Pi u<xu+1/2)/;u ∈ Z

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

Expansions at z==3Pi/2+2Pi u/;u ∈ Z && 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

Residue representations

Other series representations

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

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

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

Expansions F(sin^-1(z)|m) at m==1

Other expansions