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relation to Riemann zeta function

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1: 25.17 Physical Applications
§25.17 Physical Applications
2: 8.22 Mathematical Applications
§8.22(ii) Riemann Zeta Function and Incomplete Riemann Zeta Function
The Debye functions 0 x t n ( e t - 1 ) - 1 d t and x t n ( e t - 1 ) - 1 d t are closely related to the incomplete Riemann zeta function and the Riemann zeta function. …
3: 20.9 Relations to Other Functions
§20.9(iii) Riemann Zeta Function
4: 24.17 Mathematical Applications
§24.17(iii) Number Theory
5: 24.4 Basic Properties
§24.4(ix) Relations to Other Functions
For the relation of Bernoulli numbers to the Riemann zeta function see §25.6, and to the Eulerian numbers see (26.14.11).
6: 25.12 Polylogarithms
The special case z = 1 is the Riemann zeta function: ζ ( s ) = Li s ( 1 ) . … Further properties include …
7: 25.6 Integer Arguments
§25.6(i) Function Values
8: 25.11 Hurwitz Zeta Function
The Riemann zeta function is a special case: …
9: 25.10 Zeros
§25.10(i) Distribution
The functional equation (25.4.1) implies ζ ( - 2 n ) = 0 for n = 1 , 2 , 3 , . … Calculations relating to the zeros on the critical line make use of the real-valued function
§25.10(ii) Riemann–Siegel Formula
10: 25.16 Mathematical Applications
which is related to the Riemann zeta function by …