Riemann%E2%80%93Siegel%20formula
(0.003 seconds)
11—20 of 351 matching pages
11: 25.6 Integer Arguments
…
►
§25.6(i) Function Values
… ►
25.6.3
.
►
25.6.4
.
…
►
§25.6(ii) Derivative Values
… ►§25.6(iii) Recursion Formulas
…12: 25.19 Tables
…
►
•
…
►
•
►
•
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.
13: 15.11 Riemann’s Differential Equation
§15.11 Riemann’s Differential Equation
►§15.11(i) Equations with Three Singularities
… ►The complete set of solutions of (15.11.1) is denoted by Riemann’s -symbol: … ►§15.11(ii) Transformation Formulas
… ►for arbitrary and .14: 25.2 Definition and Expansions
§25.2 Definition and Expansions
… ►Elsewhere is defined by analytic continuation. … ►§25.2(ii) Other Infinite Series
… ►§25.2(iii) Representations by the Euler–Maclaurin Formula
… ►§25.2(iv) Infinite Products
…15: 25.16 Mathematical Applications
§25.16 Mathematical Applications
… ►which is related to the Riemann zeta function by … ►The Riemann hypothesis is equivalent to the statement … ►§25.16(ii) Euler Sums
… ►which satisfies the reciprocity law …16: 25.7 Integrals
§25.7 Integrals
►For definite integrals of the Riemann zeta function see Prudnikov et al. (1986b, §2.4), Prudnikov et al. (1992a, §3.2), and Prudnikov et al. (1992b, §3.2).17: 25.17 Physical Applications
§25.17 Physical Applications
►Analogies exist between the distribution of the zeros of on the critical line and of semiclassical quantum eigenvalues. This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999). …18: 21.3 Symmetry and Quasi-Periodicity
…
►
§21.3(i) Riemann Theta Functions
… ► ►§21.3(ii) Riemann Theta Functions with Characteristics
… ► …For Riemann theta functions with half-period characteristics, …19: 25.5 Integral Representations
§25.5 Integral Representations
… ►
25.5.1
.
…
►
25.5.5
.
…
►
25.5.19
.
►