Series representations

Generalized power series

Expansions at nu==+-n

Expansions at generic point z==z₀

For the function itself

Expansions on branch cuts

For the function itself

Expansions at z==0

For the function itself

General case

Special cases

For small integer powers of the function

For the second power

Asymptotic series expansions

Expansions inside Stokes sectors

Expansions containing z->infinity

In exponential form ||| In exponential form

In trigonometric form ||| In trigonometric form

Expansions containing z->-infinity

In exponential form ||| In exponential form

In trigonometric form ||| In trigonometric form

Expansions for any z in exponential form

Using exponential function with branch cut-containing arguments

Using exponential function with branch cut-free arguments

Expansions for any z in trigonometric form

Using trigonometric functions with branch cut-containing arguments

Using trigonometric functions with branch cut-free arguments

Residue representations