Stieltjes constants (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Stieltjes constants" in English language version.

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12arxiv.org

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4stackexchange.com

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3harvard.edu

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3semanticscholar.org

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2colgate.edu

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1plouffe.fr

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1springer.com

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1researchgate.net

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arxiv.org

Coffey, Mark W. (2009). "Series representations for the Stieltjes constants". arXiv:0905.1111 [math-ph].
Blagouchine, Iaroslav V. (2015). "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: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009. And vol. 151, pp. 276-277, 2015. arXiv:1401.3724
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π$ ⁻² and into the formal enveloping series with rational coefficients only". Journal of Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012. Corrigendum: vol. 173, pp. 631-632, 2017.
Donal F. Connon Some applications of the Stieltjes constants, arXiv:0901.2083
Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions" (PDF). INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. doi:10.5281/zenodo.10581385.
Lazhar Fekih-Ahmed. A New Effective Asymptotic Formula for the Stieltjes Constants, arXiv:1407.5567
Krzysztof Maślanka. Asymptotic Properties of Stieltjes Constants. Computational Methods in Science and Technology, vol. 28 (2022), p.123-131; https://arxiv.org/abs/2210.07244v1
Johansson, Fredrik (2015). "Rigorous high-precision computation of the Hurwitz zeta function and its derivatives". Num. Alg. 69 (2): 253–570. arXiv:1309.2877. doi:10.1007/s11075-014-9893-1. S2CID 10344040.
Johansson, Fredrik; Blagouchine, Iaroslav (2019). "Computing Stieltjes constants using complex integration". Mathematics of Computation. 88 (318): 1829–1850. arXiv:1804.01679. doi:10.1090/mcom/3401. S2CID 4619883.
Connon, Donal F. (2009). "New proofs of the duplication and multiplication formulae for the gamma and the Barnes double gamma functions". arXiv:0903.4539 [math.CA].
Mark W. Coffey Functional equations for the Stieltjes constants, arXiv:1402.3746
Donal F. Connon The difference between two Stieltjes constants, arXiv:0906.0277

colgate.edu

math.colgate.edu

Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions" (PDF). INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. doi:10.5281/zenodo.10581385.
Actually Blagouchine gives more general formulas, which are valid for the generalized Stieltjes constants as well.

doi.org

Coffey, Mark W. (2010). "Addison-type series representation for the Stieltjes constants". J. Number Theory. 130 (9): 2049–2064. doi:10.1016/j.jnt.2010.01.003.
Blagouchine, Iaroslav V. (2015). "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: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009. And vol. 151, pp. 276-277, 2015. arXiv:1401.3724
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π$ ⁻² and into the formal enveloping series with rational coefficients only". Journal of Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012. Corrigendum: vol. 173, pp. 631-632, 2017.
Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions" (PDF). INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. doi:10.5281/zenodo.10581385.
Choudhury, B. K. (1995). "The Riemann zeta-function and its derivatives". Proc. R. Soc. A. 450 (1940): 477–499. Bibcode:1995RSPSA.450..477C. doi:10.1098/rspa.1995.0096. S2CID 124034712.
Keiper, J.B. (1992). "Power series expansions of Riemann ζ-function". Math. Comp. 58 (198): 765–773. Bibcode:1992MaCom..58..765K. doi:10.1090/S0025-5718-1992-1122072-5.
Kreminski, Rick (2003). "Newton-Cotes integration for approximating Stieltjes generalized Euler constants". Math. Comp. 72 (243): 1379–1397. Bibcode:2003MaCom..72.1379K. doi:10.1090/S0025-5718-02-01483-7.
Johansson, Fredrik (2015). "Rigorous high-precision computation of the Hurwitz zeta function and its derivatives". Num. Alg. 69 (2): 253–570. arXiv:1309.2877. doi:10.1007/s11075-014-9893-1. S2CID 10344040.
Johansson, Fredrik; Blagouchine, Iaroslav (2019). "Computing Stieltjes constants using complex integration". Mathematics of Computation. 88 (318): 1829–1850. arXiv:1804.01679. doi:10.1090/mcom/3401. S2CID 4619883.

harvard.edu

ui.adsabs.harvard.edu

Choudhury, B. K. (1995). "The Riemann zeta-function and its derivatives". Proc. R. Soc. A. 450 (1940): 477–499. Bibcode:1995RSPSA.450..477C. doi:10.1098/rspa.1995.0096. S2CID 124034712.
Keiper, J.B. (1992). "Power series expansions of Riemann ζ-function". Math. Comp. 58 (198): 765–773. Bibcode:1992MaCom..58..765K. doi:10.1090/S0025-5718-1992-1122072-5.
Kreminski, Rick (2003). "Newton-Cotes integration for approximating Stieltjes generalized Euler constants". Math. Comp. 72 (243): 1379–1397. Bibcode:2003MaCom..72.1379K. doi:10.1090/S0025-5718-02-01483-7.

plouffe.fr

Simon Plouffe. Stieltjes Constants, from 0 to 78, 256 digits each

researchgate.net

Iaroslav V. Blagouchine Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results. The Ramanujan Journal, vol. 35, no. 1, pp. 21-110, 2014. Erratum-Addendum: vol. 42, pp. 777-781, 2017. PDF

semanticscholar.org

api.semanticscholar.org

Choudhury, B. K. (1995). "The Riemann zeta-function and its derivatives". Proc. R. Soc. A. 450 (1940): 477–499. Bibcode:1995RSPSA.450..477C. doi:10.1098/rspa.1995.0096. S2CID 124034712.
Johansson, Fredrik (2015). "Rigorous high-precision computation of the Hurwitz zeta function and its derivatives". Num. Alg. 69 (2): 253–570. arXiv:1309.2877. doi:10.1007/s11075-014-9893-1. S2CID 10344040.
Johansson, Fredrik; Blagouchine, Iaroslav (2019). "Computing Stieltjes constants using complex integration". Mathematics of Computation. 88 (318): 1829–1850. arXiv:1804.01679. doi:10.1090/mcom/3401. S2CID 4619883.

springer.com

link.springer.com

Iaroslav V. Blagouchine Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results. The Ramanujan Journal, vol. 35, no. 1, pp. 21-110, 2014. Erratum-Addendum: vol. 42, pp. 777-781, 2017. PDF