Hurwitz criterion
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1: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
►§25.11(i) Definition
… ►§25.11(ii) Graphics
… ►§25.11(vi) Derivatives
… ►§25.11(ix) Integrals
…2: 1.11 Zeros of Polynomials
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Hurwitz Criterion
…3: 21.10 Methods of Computation
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Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.
4: 25.13 Periodic Zeta Function
5: 25.18 Methods of Computation
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§25.18(i) Function Values and Derivatives
… ►Calculations relating to derivatives of and/or can be found in Apostol (1985a), Choudhury (1995), Miller and Adamchik (1998), and Yeremin et al. (1988). ►For the Hurwitz zeta function see Spanier and Oldham (1987, p. 653) and Coffey (2009). …6: 25.1 Special Notation
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►The main related functions are the Hurwitz zeta function , the dilogarithm , the polylogarithm (also known as Jonquière’s function ), Lerch’s transcendent , and the Dirichlet -functions .
7: Bibliography B
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On the Hurwitz zeta-function.
Rocky Mountain J. Math. 2 (1), pp. 151–157.
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Criterion for Existence of a Bound State In One Dimension.
American Journal of Physics 68 (2), pp. 160–161.
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8: 8.15 Sums
9: 25.19 Tables
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Fletcher et al. (1962, §22.1) lists many sources for earlier tables of for both real and complex . §22.133 gives sources for numerical values of coefficients in the Riemann–Siegel formula, §22.15 describes tables of values of , and §22.17 lists tables for some Dirichlet -functions for real characters. For tables of dilogarithms, polylogarithms, and Clausen’s integral see §§22.84–22.858.