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Chapter 25
Zeta and Related Functions
Notes:
The main references used in writing this chapter are
Apostol (
1976
)
,
Erdélyi
et al.
(
1953a
)
, and
Titchmarsh (
1986b
)
. For additional bibliographic reading see
Edwards (
1974
)
,
Ivić (
1985
)
,
Karatsuba and Voronin (
1992
)
.
Referenced by:
§5.11(ii)
,
§5.17
,
§5.7(i)
,
¶
‣
§5.9(i)
,
Tom M. Apostol
,
§
‣
§
Software Cross Index
Permalink:
http://dlmf.nist.gov/25
T. M. Apostol
California Institute of Technology, Pasadena, California.
Notation
25.1
Special Notation
Riemann Zeta Function
25.2
Definition and Expansions
25.3
Graphics
25.4
Reflection Formulas
25.5
Integral Representations
25.6
Integer Arguments
25.7
Integrals
25.8
Sums
25.9
Asymptotic Approximations
25.10
Zeros
Related Functions
25.11
Hurwitz Zeta Function
25.12
Polylogarithms
25.13
Periodic Zeta Function
25.14
Lerch’s Transcendent
25.15
Dirichlet
-functions
Applications
25.16
Mathematical Applications
25.17
Physical Applications
Computation
25.18
Methods of Computation
25.19
Tables
25.20
Approximations
25.21
Software