Series representations

Generalized power series

Expansions at generic point z==z₀

For the function itself

Expansions on branch cuts ||| Expansions on branch cuts

For the function itself

For the function itself

Expansions at z==0

Case of simple poles

Case of poles of order r in the points -b_r-k/;r ∈ {1,2,3,4} && k ∈ N

Expansions at z==(-1)^m+n-q for p==q

The general formula for arbitrary z

The general formula for psi_q ∉ Z in the particular case |z|>1

The major terms in the general formulas for expansions of function p==q at z==(-1)^m+n-q

Expansions at z==infinity

Case of simple poles

Case of poles of order r in the points -a_r+k/;r ∈ {1,2,3,4} && k ∈ N⁺

Asymptotic series expansions at z==0 for q<p

Expansions for p==q+1

Expansions for p==q+2

Expansions for p>q+2

Asymptotic series expansions at z==infinity for q>p

Expansions for q==p+1

Expansions for q==p+2

Expansions for q>p+2

General formulas of asymptotic series expansions

Main terms of asymptotic expansions

Expansions at z==0

Expansions at z==(-1)^m+n-q for p==q

Expansions at z==infinity

Residue representations