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

Generic formulas for main term

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 hyperbolic form ||| In hyperbolic form

Expansions containing z->-infinity

In exponential form ||| In exponential form

In hyperbolic form ||| In hyperbolic 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