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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia

Dokl. RAN. Math. Inf. Proc. Upr., 2020, Volume 494, Pages 48–52 (Mi danma116)

Representations of $\zeta(2n+1)$ and related numbers in the form of definite integrals and rapidly convergent series
K. M. Mirzoev, T. A. Safonova

References

1. Abramowitz M., Stegun I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, N.Y., 1972, 1046 pp.  mathscinet
2. Finch S.R., Mathematical constants, Cambridge University Press, N.Y., 2003, 602 pp.  mathscinet  zmath
3. NIST Handbook of Mathematcal Functuios, N.Y., Cambridge, 2010, 951 pp.
4. Cvijovic D., Klinowski J., “Integral Representations of the Riemann Zeta Function for Odd-Integer Arguments”, J. Computational and Applied Mathematics, 142 (2002), 435–439  crossref  mathscinet  zmath
5. Zudilin V.V., “Ob irratsionalnosti znachenii dzeta-funktsii Rimana”, Izvestiya RAN. Seriya matem., 66:3 (2002), 49–102  mathnet  crossref  mathscinet  zmath
6. Srivastava H.M., “The Zeta and Related Functions: Recent Developments”, J. Advanced Engineering and Computation, 3:1 (2019), 329–354  crossref  mathscinet
7. Mirzoev K.A., Safonova T.A., “Funktsiya Grina obyknovennykh differentsialnykh operatorov i integralnoe predstavlenie summ nekotorykh stepennykh ryadov”, DAN, 482:5 (2018), 500–503  zmath
8. Mirzoev K.A.,Safonova T.A., “Ob integralnom predstavlenii summ nekotorykh stepennykh ryadov”, Matem. zametki, 106:3 (2019), 470–475  mathnet  crossref  mathscinet  zmath
9. Mirzoev K.A., Safonova T.A., “Obyknovennye differentsialnye operatory i integralnoe predstavlenie summ nekotorykh stepennykh ryadov”, Tr. MMO, 80, no. 2, 2019, 157–177  mathnet  zmath
10. Prudnikov A.P., Brychkov Yu.A., Marichev O.I., Integraly i ryady. Elementarnye funktsii, v. 1, Fizmatlit, M., 2002, 632 pp.  mathscinet
11. Mirzoev K.A., Safonova T.A., “Integralnoe predstavlenie summ nekotorykh ryadov, svyazannykh so spetsialnymi funktsiyami”, Matem. zametki, 108:2 (2020), 632–637  mathnet  zmath
12. Berndt B.C., Ramanujan's Notebooks, v. I, Springer Verlag, N.Y., 1985, 357 pp.  mathscinet
13. Srivastava H.M., Glasser M.L., Adamchik V.S., “Some Definite Integrals Associated with the Riemann Zeta Function”, J. for Analysis and its Applications, 19:3 (2000), 831–846  mathscinet  zmath
14. Cvijovic D., Klinowski J., “New Rapidly Convergent Series Representations for $\zeta (2n + 1)$”, Proc. Amer. Math. Society, 125:5 (1997), 1263–1271  crossref  mathscinet  zmath


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