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meromorphic function

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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: 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 . …
5: 5.2 Definitions
It is a meromorphic function with no zeros, and with simple poles of residue ( - 1 ) n / n ! at z = - n . …
6: 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. … …
7: 2.5 Mellin Transform Methods
If f ( 1 - z ) and h ( z ) can be continued analytically to meromorphic functions in a left half-plane, and if the contour z = c can be translated to z = d with d < c , then …Similarly, if f ( 1 - z ) and h ( z ) can be continued analytically to meromorphic functions in a right half-plane, and if the vertical line of integration can be translated to the right, then we obtain an asymptotic expansion for I ( x ) for large values of x . … Furthermore, f 1 ( z ) can be continued analytically to a meromorphic function on the entire z -plane, whose singularities are simple poles at - α s , s = 0 , 1 , 2 , , with principal part … Similarly, if κ = 0 in (2.5.18), then h 2 ( z ) can be continued analytically to a meromorphic function on the entire z -plane with simple poles at β s , s = 0 , 1 , 2 , , with principal part … Similarly, since h 2 ( z ) can be continued analytically to a meromorphic function (when κ = 0 ) or to an entire function (when κ 0 ), we can choose ρ so that h 2 ( z ) has no poles in 1 < z ρ < 2 . …
8: 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 ,
9: 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. …
10: 8.21 Generalized Sine and Cosine Integrals
Furthermore, si ( a , z ) and ci ( a , z ) are entire functions of a , and Si ( a , z ) and Ci ( a , z ) are meromorphic functions of a with simple poles at a = - 1 , - 3 , - 5 , and a = 0 , - 2 , - 4 , , respectively. …