Series representations

Generalized power series

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

Asymptotic series expansions

Expansions inside Stokes sectors

Expansions containing z->infinity

In exponential form ||| In exponential form

In hyperbolic form ||| In hyperbolic form

Containing Bessel functions

Expansions containing z->-infinity

In exponential form ||| In exponential form

In hyperbolic form ||| In hyperbolic form

The general formulas

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 and hyperbolic forms

Using trigonometric functions with branch cut-containing arguments

Using hyperbolic functions with branch cut-free arguments

Residue representations

Other series representations