Note sur la série $\sum _{n=1}^{\infty } \frac{x^n}{n^s}$

Jonquière, A.

doi:10.24033/bsmf.392

Note sur la série

\sum_{n = 1}^{\infty} \frac{x^{n}}{n^{s}}

Jonquière, A.

Bulletin de la Société Mathématique de France, Tome 17 (1889), pp. 142-152.

JFM

DOI : 10.24033/bsmf.392

@article{BSMF_1889__17__142_1,
     author = {Jonqui\`ere, A.},
     title = {Note sur la s\'erie $\sum _{n=1}^{\infty } \frac{x^n}{n^s}$},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {142--152},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {17},
     year = {1889},
     doi = {10.24033/bsmf.392},
     language = {fr},
     url = {https://www.numdam.org/articles/10.24033/bsmf.392/}
}

TY  - JOUR
AU  - Jonquière, A.
TI  - Note sur la série $\sum _{n=1}^{\infty } \frac{x^n}{n^s}$
JO  - Bulletin de la Société Mathématique de France
PY  - 1889
SP  - 142
EP  - 152
VL  - 17
PB  - Société mathématique de France
UR  - https://www.numdam.org/articles/10.24033/bsmf.392/
DO  - 10.24033/bsmf.392
LA  - fr
ID  - BSMF_1889__17__142_1
ER  -

%0 Journal Article
%A Jonquière, A.
%T Note sur la série $\sum _{n=1}^{\infty } \frac{x^n}{n^s}$
%J Bulletin de la Société Mathématique de France
%D 1889
%P 142-152
%V 17
%I Société mathématique de France
%U https://www.numdam.org/articles/10.24033/bsmf.392/
%R 10.24033/bsmf.392
%G fr
%F BSMF_1889__17__142_1

Jonquière, A. Note sur la série $\sum _{n=1}^{\infty } \frac{x^n}{n^s}$. Bulletin de la Société Mathématique de France, Tome 17 (1889), pp. 142-152. doi : 10.24033/bsmf.392. https://www.numdam.org/articles/10.24033/bsmf.392/

Bibliographie
Cité par

Wang, Kun; Lu, Zhaolian; Yao, Zeqi; He, Xionglei; Hu, Zheng; Zhou, Da Single-cell phylodynamic inference of stem cell differentiation and tumor evolution, Cell Systems (2025), p. 101244 | DOI:10.1016/j.cels.2025.101244
Genčev, Marian Generalized Mneimneh sums and their application to multiple polylogarithms, Discrete Mathematics, Volume 348 (2025) no. 2, p. 114318 | DOI:10.1016/j.disc.2024.114318
Sofo, Anthony; Pain, Jean-Christophe; Scharaschkin, Victor A family of polylogarithmic integrals, Journal of Applied Analysis (2025) | DOI:10.1515/jaa-2024-0133
Dahne, Joel Highest cusped waves for the fractional KdV equations, Journal of Differential Equations, Volume 401 (2024), p. 550 | DOI:10.1016/j.jde.2024.05.016
Akemann, Gernot; Byun, Sung-Soo; Ebke, Markus; Schehr, Grégory Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble, Journal of Physics A: Mathematical and Theoretical, Volume 56 (2023) no. 49, p. 495202 | DOI:10.1088/1751-8121/ad0885
Pepino, Rafael Tristão Acceleration of sequences with transformations involving hypergeometric functions, Numerical Algorithms, Volume 92 (2023) no. 1, p. 893 | DOI:10.1007/s11075-022-01334-7
Liu, Yiqun; Zhai, Liangjun; Yan, Songsong; Wang, Di; Wan, Xiangang Magnon-magnon interaction in monolayer MnBi2Te4, Physical Review B, Volume 108 (2023) no. 17 | DOI:10.1103/physrevb.108.174425
Kato, Masaki Parity result for q- and elliptic analogues of multiple polylogarithms, Research in Number Theory, Volume 9 (2023) no. 2 | DOI:10.1007/s40993-023-00452-y
Schoger, Tanja; Spreng, Benjamin; Ingold, Gert-Ludwig; Maia Neto, Paulo A. Casimir effect between spherical objects: Proximity-force approximation and beyond using plane waves, International Journal of Modern Physics A, Volume 37 (2022) no. 19 | DOI:10.1142/s0217751x22410093
Schenk, Hermann A.G.; Melnikov, Anton; Wall, Franziska; Gaudet, Matthieu; Stolz, Michael; Schuffenhauer, David; Kaiser, Bert Electrically Actuated Microbeams: An Explicit Calculation of the Coulomb Integral in the Entire Stable and Unstable Regimes Using a Chebyshev-Edgeworth Approach, Physical Review Applied, Volume 18 (2022) no. 1 | DOI:10.1103/physrevapplied.18.014059
Lee, Dae Sik; Kim, Hye Kyung On the new type of degenerate poly-Genocchi numbers and polynomials, Advances in Difference Equations, Volume 2020 (2020) no. 1 | DOI:10.1186/s13662-020-02886-5
Kim, Hye Kyung; Jang, Lee-Chae A note on degenerate poly-Genocchi numbers and polynomials, Advances in Difference Equations, Volume 2020 (2020) no. 1 | DOI:10.1186/s13662-020-02847-y
Calixto, M; Maldonado, D; Miranda, E; Roldán, J B Modeling of the temperature effects in filamentary-type resistive switching memories using quantum point-contact theory, Journal of Physics D: Applied Physics, Volume 53 (2020) no. 29, p. 295106 | DOI:10.1088/1361-6463/ab85e5
Gerhold, Stefan; Tomovski, Živorad Asymptotic expansion of Mathieu power series and trigonometric Mathieu series, Journal of Mathematical Analysis and Applications, Volume 479 (2019) no. 2, p. 1882 | DOI:10.1016/j.jmaa.2019.07.029
Destuynder, Philippe; Fabre, Caroline Singularities Occuring in a Bimaterial with Transparent Boundary Conditions, Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering, Volume 276 (2019), p. 79 | DOI:10.1007/978-3-030-10419-1_5
del Campo, Adolfo Universal Statistics of Topological Defects Formed in a Quantum Phase Transition, Physical Review Letters, Volume 121 (2018) no. 20 | DOI:10.1103/physrevlett.121.200601
Min, Jeongwon Mean values of the Witten L-function for SU(2), Forum Mathematicum, Volume 29 (2017) no. 2, p. 457 | DOI:10.1515/forum-2015-0056
Oswald, Nicola; Steuding, Jörn Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz, From Arithmetic to Zeta-Functions (2016), p. 309 | DOI:10.1007/978-3-319-28203-9_20
Lagarias, Jeffrey C.; Li, Wen-Ching Winnie The Lerch Zeta function III. Polylogarithms and special values, Research in the Mathematical Sciences, Volume 3 (2016) no. 1 | DOI:10.1186/s40687-015-0049-2
Eckstein, Michał; Zając, Artur Asymptotic and Exact Expansions of Heat Traces, Mathematical Physics, Analysis and Geometry, Volume 18 (2015) no. 1 | DOI:10.1007/s11040-015-9197-2
Agnese, C.; Baiamonte, G.; Cammalleri, C. Modelling the occurrence of rainy days under a typical Mediterranean climate, Advances in Water Resources, Volume 64 (2014), p. 62 | DOI:10.1016/j.advwatres.2013.12.005
Svensson, Tomas; Vynck, Kevin; Adolfsson, Erik; Farina, Andrea; Pifferi, Antonio; Wiersma, Diederik S. Light diffusion in quenched disorder: Role of step correlations, Physical Review E, Volume 89 (2014) no. 2 | DOI:10.1103/physreve.89.022141
Genty, Alain; Pot, Valérie Numerical Simulation of 3D Liquid–Gas Distribution in Porous Media by a Two-Phase TRT Lattice Boltzmann Method, Transport in Porous Media, Volume 96 (2013) no. 2, p. 271 | DOI:10.1007/s11242-012-0087-9
Condon, John D. Asymptotic expansion of the difference of two Mahler measures, Journal of Number Theory, Volume 132 (2012) no. 9, p. 1962 | DOI:10.1016/j.jnt.2012.02.022
Jung, Jesper; Pedersen, Thomas G. Polarizability of nanowires at surfaces: exact solution for general geometry, Optics Express, Volume 20 (2012) no. 4, p. 3663 | DOI:10.1364/oe.20.003663
Giuggioli, L.; Potts, J. R.; Harris, S. Brownian walkers within subdiffusing territorial boundaries, Physical Review E, Volume 83 (2011) no. 6 | DOI:10.1103/physreve.83.061138
Fermi, Davide; Pizzocchero, Livio Local Zeta Regularization and the Casimir Effect, Progress of Theoretical Physics, Volume 126 (2011) no. 3, p. 419 | DOI:10.1143/ptp.126.419
Eisinberg, A.; Fedele, G.; Ferrise, A.; Frascino, D. On an integral representation of a class of Kapteyn (Fourier–Bessel) series: Kepler’s equation, radiation problems and Meissel’s expansion, Applied Mathematics Letters, Volume 23 (2010) no. 11, p. 1331 | DOI:10.1016/j.aml.2010.06.026
Vepštas, Linas An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions, Numerical Algorithms, Volume 47 (2008) no. 3, p. 211 | DOI:10.1007/s11075-007-9153-8
Sondow, Jonathan; Hadjicostas, Petros The generalized-Euler-constant function γ(z) and a generalization of Somos's quadratic recurrence constant, Journal of Mathematical Analysis and Applications, Volume 332 (2007) no. 1, p. 292 | DOI:10.1016/j.jmaa.2006.09.081
Apostol, Tom M Dirichlet L-functions and character power sums, Journal of Number Theory, Volume 2 (1970) no. 2, p. 223 | DOI:10.1016/0022-314x(70)90022-3
Dingle, R. B. The Fermi-Dirac integrals $F_{p} (η) = (p!)^{- 1} \int_{0}^{\infty} ε^{p} (e^{ε - η} + 1)^{- 1} d ε$ , Applied Scientific Research, Section B, Volume 6 (1957) no. 1, p. 225 | DOI:10.1007/bf02920379
Dingle, R. B. The Bose-Einstein integrals $B_{p} (η) = (p!)^{- 1} \int_{0}^{\infty} ε^{p} (e^{ε - η} - 1)^{- 1} d ε$ , Applied Scientific Research, Section B, Volume 6 (1957) no. 1, p. 240 | DOI:10.1007/bf02920380

Cité par 33 documents. Sources : Crossref