periodic zeta function
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1: 25.13 Periodic Zeta Function
§25.13 Periodic Zeta Function
►The notation is used for the polylogarithm with real: ►
25.13.1
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►Also,
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25.13.2
, ,
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2: 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
.
3: 23.2 Definitions and Periodic Properties
4: 25.16 Mathematical Applications
5: 25.11 Hurwitz Zeta Function
6: 25.2 Definition and Expansions
7: 31.2 Differential Equations
8: Bibliography K
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The Riemann Zeta-Function.
de Gruyter Expositions in Mathematics, Vol. 5, Walter de Gruyter & Co., Berlin.
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Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
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The Riemann Zeta-Function and Quantum Chaology.
In Quantum Chaos (Varenna, 1991),
Proc. Internat. School of Phys. Enrico Fermi, CXIX, pp. 145–185.
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Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function.
Math. Comp. 24 (111), pp. 679–696.
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Complex zeros of two incomplete Riemann zeta functions.
Math. Comp. 26 (118), pp. 551–565.
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9: Errata
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Equations (25.11.6), (25.11.19), and (25.11.20)
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Originally all six integrands in these equations were incorrect because their numerators contained the function . The correct function is . The new equations are:
25.11.6
, ,
Reported 2016-05-08 by Clemens Heuberger.
25.11.19
, ,
Reported 2016-06-27 by Gergő Nemes.
25.11.20
, ,
Reported 2016-06-27 by Gergő Nemes.
10: 24.17 Mathematical Applications
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