periodic%20Euler%20functions

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1: 24.2 Definitions and Generating Functions

§24.2 Definitions and Generating Functions

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§24.2(ii) Euler Numbers and Polynomials

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§24.2(iii) Periodic Bernoulli and Euler Functions

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${\tilde{E}}_n\left(x\right)=E_n\left(x\right)$ , ,

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${\tilde{E}}_n\left(x+1\right)=-{\tilde{E}}_n\left(x\right)$ , $x\in ℝ$.

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2: 25.11 Hurwitz Zeta Function

§25.11 Hurwitz Zeta Function

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§25.11(i) Definition

… ►The Riemann zeta function is a special case: … ►

§25.11(iii) Representations by the Euler–Maclaurin Formula

… ►For ${\tilde{B}}_n\left(x\right)$ see §24.2(iii). …

3: Bibliography B

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A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

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1st item.

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

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Document, Code

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1st item, 4th item.

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Periodic Bernoulli numbers, summation formulas and applications. In Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), pp. 143–189.

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§24.16(iii), §24.8(ii).

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Bessel functions and modular relations of higher type and hyperbolic differential equations. Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

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§35.5(i).

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Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems. J. Phys. A 34 (40), pp. 8199–8220.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

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§29.19(i).

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4: Bibliography K

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Heat conduction and diffusion in a fluid medium with a periodic flow. I. Determination of the wave transfer coefficient in a tube, slot, and canal. Akad. Nauk SSSR. Žurnal Eksper. Teoret. Fiz. 21, pp. 964–978.

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External Links:

MathReview (N. A. Hall)

Referenced by:

§10.73(v).

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

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1st item.

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Periodic Orbits, Spectral Statistics, and the Riemann Zeros. In Supersymmetry and Trace Formulae: Chaos and Disorder, J. P. Keating, D. E. Khmelnitskii, and I. V. Lerner (Eds.), pp. 1–15.

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§25.17.

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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An algebraic-geometrical construction of the Zakharov-Shabat equations and their periodic solutions. Sov. Math. Doklady 17, pp. 394–397.

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External Links:

ZentralBlatt

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Figure 21.9.2, Figure 21.9.2, §21.9, §21.9, Sidebar 21.SB2.

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