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1: 21.8 Abelian Functions
An Abelian function is a 2 g -fold periodic, meromorphic function of g complex variables. …
2: 13.5 Continued Fractions
This continued fraction converges to the meromorphic function of z on the left-hand side everywhere in . For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980). … This continued fraction converges to the meromorphic function of z on the left-hand side throughout the sector | ph z | < π . …
3: 13.17 Continued Fractions
This continued fraction converges to the meromorphic function of z on the left-hand side for all z . For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980). … This continued fraction converges to the meromorphic function of z on the left-hand side throughout the sector | ph z | < π . …
4: 5.2 Definitions
It is a meromorphic function with no zeros, and with simple poles of residue ( - 1 ) n / n ! at z = - n . … ψ ( z ) is meromorphic with simple poles of residue - 1 at z = - n . …
5: 4.14 Definitions and Periodicity
The functions tan z , csc z , sec z , and cot z are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7). …
6: 22.17 Moduli Outside the Interval [0,1]
When z is fixed each of the twelve Jacobian elliptic functions is a meromorphic function of k 2 . …
7: 23.2 Definitions and Periodic Properties
( z ) and ζ ( z ) are meromorphic functions with poles at the lattice points. … Hence ( z ) is an elliptic function, that is, ( z ) is meromorphic and periodic on a lattice; equivalently, ( z ) is meromorphic and has two periods whose ratio is not real. …
8: 22.2 Definitions
Each is meromorphic in z for fixed k , with simple poles and simple zeros, and each is meromorphic in k for fixed z . …
9: 25.2 Definition and Expansions
It is a meromorphic function whose only singularity in is a simple pole at s = 1 , with residue 1. …
25.2.4 ζ ( s ) = 1 s - 1 + n = 0 ( - 1 ) n n ! γ n ( s - 1 ) n ,
10: 1.10 Functions of a Complex Variable
A function whose only singularities, other than the point at infinity, are poles is called a meromorphic function. … …