Hurwitz zeta function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Hurwitz zeta function" in English language version.

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archive.org

Hurwitz, Adolf (1882). "Einige Eigenschaften der Dirichlet'schen Functionen ${\textstyle F(s)=\sum \left({\frac {D}{n}}\right)\cdot {\frac {1}{n}}}$ , die bei der Bestimmung der Classenanzahlen binärer quadratischer Formen auftreten". Zeitschrift für Mathematik und Physik (in German). 27: 86–101.

arxiv.org

Blagouchine, I.V. (2014). "A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations". Journal of Number Theory. 148. Elsevier: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009.
Vepstas, Linas (2007). "An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions". Numerical Algorithms. 47 (3): 211–252. arXiv:math/0702243. Bibcode:2008NuAlg..47..211V. doi:10.1007/s11075-007-9153-8. S2CID 15131811.

doi.org

See the references in Section 4 of: Kanemitsu, S.; Tanigawa, Y.; Tsukada, H.; Yoshimoto, M. (2007). "Contributions to the theory of the Hurwitz zeta-function". Hardy-Ramanujan Journal. 30: 31–55. doi:10.46298/hrj.2007.159. Zbl 1157.11036.
Fine, N. J. (June 1951). "Note on the Hurwitz Zeta-Function". Proceedings of the American Mathematical Society. 2 (3): 361–364. doi:10.2307/2031757. JSTOR 2031757. Zbl 0043.07802.
Berndt, Bruce C. (Winter 1972). "On the Hurwitz zeta-function". Rocky Mountain Journal of Mathematics. 2 (1): 151–158. doi:10.1216/RMJ-1972-2-1-151. Zbl 0229.10023.
Blagouchine, I.V. (2014). "A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations". Journal of Number Theory. 148. Elsevier: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009.
Hasse, Helmut (1930), "Ein Summierungsverfahren für die Riemannsche ζ-Reihe", Mathematische Zeitschrift, 32 (1): 458–464, doi:10.1007/BF01194645, JFM 56.0894.03, S2CID 120392534
Vepstas, Linas (2007). "An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions". Numerical Algorithms. 47 (3): 211–252. arXiv:math/0702243. Bibcode:2008NuAlg..47..211V. doi:10.1007/s11075-007-9153-8. S2CID 15131811.
Jacek Klinowski, Djurdje Cvijović (1999). "Values of the Legendre chi and Hurwitz zeta functions at rational arguments". Mathematics of Computation. 68 (228): 1623–1631. Bibcode:1999MaCom..68.1623C. doi:10.1090/S0025-5718-99-01091-1.
Berndt, Bruce C. (1985). "The Gamma Function and the Hurwitz Zeta-Function". The American Mathematical Monthly. 92 (2): 126–130. doi:10.2307/2322640. JSTOR 2322640.
Davenport, H. & Heilbronn, H. (1936), "On the zeros of certain Dirichlet series", Journal of the London Mathematical Society, 11 (3): 181–185, doi:10.1112/jlms/s1-11.3.181, Zbl 0014.21601
Cassels, J. W. S. (1961), "Footnote to a note of Davenport and Heilbronn", Journal of the London Mathematical Society, 36 (1): 177–184, doi:10.1112/jlms/s1-36.1.177, Zbl 0097.03403
Given by Cvijović, Djurdje & Klinowski, Jacek (1999), "Values of the Legendre chi and Hurwitz zeta functions at rational arguments", Mathematics of Computation, 68 (228): 1623–1630, Bibcode:1999MaCom..68.1623C, doi:10.1090/S0025-5718-99-01091-1
Schwinger, J. (1951), "On gauge invariance and vacuum polarization", Physical Review, 82 (5): 664–679, Bibcode:1951PhRv...82..664S, doi:10.1103/PhysRev.82.664

eudml.org

Hasse, Helmut (1930), "Ein Summierungsverfahren für die Riemannsche ζ-Reihe", Mathematische Zeitschrift, 32 (1): 458–464, doi:10.1007/BF01194645, JFM 56.0894.03, S2CID 120392534

harvard.edu

ui.adsabs.harvard.edu

Vepstas, Linas (2007). "An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions". Numerical Algorithms. 47 (3): 211–252. arXiv:math/0702243. Bibcode:2008NuAlg..47..211V. doi:10.1007/s11075-007-9153-8. S2CID 15131811.
Jacek Klinowski, Djurdje Cvijović (1999). "Values of the Legendre chi and Hurwitz zeta functions at rational arguments". Mathematics of Computation. 68 (228): 1623–1631. Bibcode:1999MaCom..68.1623C. doi:10.1090/S0025-5718-99-01091-1.
Given by Cvijović, Djurdje & Klinowski, Jacek (1999), "Values of the Legendre chi and Hurwitz zeta functions at rational arguments", Mathematics of Computation, 68 (228): 1623–1630, Bibcode:1999MaCom..68.1623C, doi:10.1090/S0025-5718-99-01091-1
Schwinger, J. (1951), "On gauge invariance and vacuum polarization", Physical Review, 82 (5): 664–679, Bibcode:1951PhRv...82..664S, doi:10.1103/PhysRev.82.664

ipython.org

nbviewer.ipython.org

"Jupyter Notebook Viewer".

jstor.org

Fine, N. J. (June 1951). "Note on the Hurwitz Zeta-Function". Proceedings of the American Mathematical Society. 2 (3): 361–364. doi:10.2307/2031757. JSTOR 2031757. Zbl 0043.07802.
Berndt, Bruce C. (1985). "The Gamma Function and the Hurwitz Zeta-Function". The American Mathematical Monthly. 92 (2): 126–130. doi:10.2307/2322640. JSTOR 2322640.

mixedmath.wordpress.com

Lowry, David (8 February 2013). "Hurwitz Zeta is a sum of Dirichlet L functions, and vice-versa". mixedmath. Retrieved 8 February 2013.

semanticscholar.org

api.semanticscholar.org

Hasse, Helmut (1930), "Ein Summierungsverfahren für die Riemannsche ζ-Reihe", Mathematische Zeitschrift, 32 (1): 458–464, doi:10.1007/BF01194645, JFM 56.0894.03, S2CID 120392534
Vepstas, Linas (2007). "An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions". Numerical Algorithms. 47 (3): 211–252. arXiv:math/0702243. Bibcode:2008NuAlg..47..211V. doi:10.1007/s11075-007-9153-8. S2CID 15131811.

zbmath.org

See the references in Section 4 of: Kanemitsu, S.; Tanigawa, Y.; Tsukada, H.; Yoshimoto, M. (2007). "Contributions to the theory of the Hurwitz zeta-function". Hardy-Ramanujan Journal. 30: 31–55. doi:10.46298/hrj.2007.159. Zbl 1157.11036.
Fine, N. J. (June 1951). "Note on the Hurwitz Zeta-Function". Proceedings of the American Mathematical Society. 2 (3): 361–364. doi:10.2307/2031757. JSTOR 2031757. Zbl 0043.07802.
Berndt, Bruce C. (Winter 1972). "On the Hurwitz zeta-function". Rocky Mountain Journal of Mathematics. 2 (1): 151–158. doi:10.1216/RMJ-1972-2-1-151. Zbl 0229.10023.
Hasse, Helmut (1930), "Ein Summierungsverfahren für die Riemannsche ζ-Reihe", Mathematische Zeitschrift, 32 (1): 458–464, doi:10.1007/BF01194645, JFM 56.0894.03, S2CID 120392534
Kubert, Daniel S.; Lang, Serge (1981). Modular Units. Grundlehren der Mathematischen Wissenschaften. Vol. 244. Springer-Verlag. p. 13. ISBN 0-387-90517-0. Zbl 0492.12002.
Davenport, H. & Heilbronn, H. (1936), "On the zeros of certain Dirichlet series", Journal of the London Mathematical Society, 11 (3): 181–185, doi:10.1112/jlms/s1-11.3.181, Zbl 0014.21601
Cassels, J. W. S. (1961), "Footnote to a note of Davenport and Heilbronn", Journal of the London Mathematical Society, 36 (1): 177–184, doi:10.1112/jlms/s1-36.1.177, Zbl 0097.03403