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meromorphic function

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11: 13.2 Definitions and Basic Properties
M ( a , b , z ) is entire in z and a , and is a meromorphic function of b . …
12: 23.15 Definitions
A modular function f ( τ ) is a function of τ that is meromorphic in the half-plane τ > 0 , and has the property that for all 𝒜 SL ( 2 , ) , or for all 𝒜 belonging to a subgroup of SL ( 2 , ) , …
13: 25.15 Dirichlet L -functions
The notation L ( s , χ ) was introduced by Dirichlet (1837) for the meromorphic continuation of the function defined by the series …
14: 29.12 Definitions
In consequence they are doubly-periodic meromorphic functions of z . …
15: 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). …
16: 8.2 Definitions and Basic Properties
When z 0 , Γ ( a , z ) is an entire function of a , and γ ( a , z ) is meromorphic with simple poles at a = - n , n = 0 , 1 , 2 , , with residue ( - 1 ) n / n ! . …
17: 22.2 Definitions
§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 . … … The Jacobian functions are related in the following way. … In terms of Neville’s theta functions20.1) …
18: 3.5 Quadrature
which depends on function values computed previously. …
Gauss Formula for a Logarithmic Weight Function
Example
If f is meromorphic, with poles near the saddle point, then the foregoing method can be modified. …
19: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
§25.11(i) Definition
ζ ( s , a ) has a meromorphic continuation in the s -plane, its only singularity in being a simple pole at s = 1 with residue 1 . …The Riemann zeta function is a special case: …
§25.11(ii) Graphics
20: 23.3 Differential Equations
As functions of g 2 and g 3 , ( z ; g 2 , g 3 ) and ζ ( z ; g 2 , g 3 ) are meromorphic and σ ( z ; g 2 , g 3 ) is entire. …