Series representations

Generalized power series

Expansions at generic point a==a₀

For the function itself

Expansions at a==0

For the function itself

Expansions at generic point z==z₀

For the function itself

Expansions of f(z)^a at z==z₀

Expansions on branch cuts

For the function itself

Expansions at z==1

For the function itself

General case

Special cases

Expansions of (1+z)^a at z==0

For the function itself

General case

Special cases

Expansions of (1+Sum_k=1^infinityc_k z^k)^a at z==0

Expansions of (1+z)^a at z==infinity

For the function itself

General case

Special cases

Asymptotic series expansions

Residue representations

Representations of z^a

Representations of (1+z)^a