Series representations

Generalized power series

Expansions at generic point z==z₀

For the function itself

Expansions on branch cuts for p==q+1

For the function itself

Expansions at z==0

Expansions at z==1 for p==q+1

The general formulas

The logarithmic cases

The major terms in the general formula for expansions of function _q+1F_q(a₁,...,a_q+1;b₁,...,b_q;z) at z==1

Expansions at z==infinity for p==q+1

The general formulas

Case of simple poles

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

The major terms for expansions of function _q+1F_q(a₁,...,a_q+1;b₁,...,b_q;z) at z==infinity

Expansions at z==infinity for polynomial cases

Asymptotic series expansions

Expansions for q==p

Expansions for q==p+1

Expansions for q>=p+2

Expansions for ₀F₂

Expansions for ₀F₃

General formulas of asymptotic series expansions

Main terms of asymptotic expansions

Residue representations