Series representations

Generalized power series

Expansions at generic point z==z₀

For the function itself

Expansions on branch cut

For the function itself

Expansions at z==0

For the function itself

General case

Expansions at z==1

For the function itself

General case

Logarithmic cases

The major terms in the general formula for expansions at z==1

Expansions at z==infinity

For the function itself

The general formulas

Case of simple poles

Case of poles of order r in the points a_r+k/;r ∈ {2,3} && k ∈ N

The major terms at z==infinity

Expansions at z==infinity for polynomial cases

Residue representations