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11: 13.2 Definitions and Basic Properties
β–Ί M ⁑ ( a , b , z ) is entire in z and a , and is a meromorphic function of b . …
12: 23.15 Definitions
β–ΊA modular function f ⁑ ( Ο„ ) is a function of Ο„ that is meromorphic in the half-plane ⁑ Ο„ > 0 , and has the property that for all π’œ SL ⁒ ( 2 , β„€ ) , or for all π’œ belonging to a subgroup of SL ( 2 , β„€ ) , …
13: 25.15 Dirichlet L -functions
β–ΊThe notation L ⁑ ( s , Ο‡ ) was introduced by Dirichlet (1837) for the meromorphic continuation of the function defined by the series …
14: 29.12 Definitions
β–ΊIn consequence they are doubly-periodic meromorphic functions of z . …
15: 4.14 Definitions and Periodicity
β–ΊThe 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
β–ΊWhen z 0 , Ξ“ ⁑ ( a , z ) is an entire function of a , and Ξ³ ⁑ ( 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
β–ΊEach is meromorphic in z for fixed k , with simple poles and simple zeros, and each is meromorphic in k for fixed z . … … β–ΊThe Jacobian functions are related in the following way. … β–ΊIn terms of Neville’s theta functions20.1) …
18: 3.5 Quadrature
β–Ίwhich depends on function values computed previously. … β–Ί
Gauss Formula for a Logarithmic Weight Function
β–Ί
Example
β–Ί β–ΊIf 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
β–Ί
§25.11(i) Definition
β–Ί ΞΆ ⁑ ( s , a ) has a meromorphic continuation in the s -plane, its only singularity in β„‚ being a simple pole at s = 1 with residue 1 . …The Riemann zeta function is a special case: … β–Ί
§25.11(ii) Graphics
20: 23.3 Differential Equations
β–ΊAs functions of g 2 ⁑ and g 3 ⁑ , ⁑ ( z ; g 2 ⁑ , g 3 ⁑ ) and ΞΆ ⁑ ( z ; g 2 ⁑ , g 3 ⁑ ) are meromorphic and Οƒ ⁑ ( z ; g 2 ⁑ , g 3 ⁑ ) is entire. …