Sur l'équation différentielle linéaire, qui admet pour intégrale la série hypergéométrique
Annales scientifiques de l'École Normale Supérieure, Série 2, Tome 10 (1881), pp. 3-142. (Pages supplémentaires)
@article{ASENS_1881_2_10__S3_0,
author = {Goursat, \'Edouard},
title = {Sur l'\'equation diff\'erentielle lin\'eaire, qui admet pour int\'egrale la s\'erie hyperg\'eom\'etrique},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {3--142},
publisher = {Elsevier},
volume = {2e s{\'e}rie, 10},
year = {1881},
doi = {10.24033/asens.207},
language = {fr},
url = {https://www.numdam.org/articles/10.24033/asens.207/}
}
TY - JOUR AU - Goursat, Édouard TI - Sur l'équation différentielle linéaire, qui admet pour intégrale la série hypergéométrique JO - Annales scientifiques de l'École Normale Supérieure PY - 1881 SP - 3 EP - 142 VL - 10 PB - Elsevier UR - https://www.numdam.org/articles/10.24033/asens.207/ DO - 10.24033/asens.207 LA - fr ID - ASENS_1881_2_10__S3_0 ER -
%0 Journal Article %A Goursat, Édouard %T Sur l'équation différentielle linéaire, qui admet pour intégrale la série hypergéométrique %J Annales scientifiques de l'École Normale Supérieure %D 1881 %P 3-142 %V 10 %I Elsevier %U https://www.numdam.org/articles/10.24033/asens.207/ %R 10.24033/asens.207 %G fr %F ASENS_1881_2_10__S3_0
Goursat, Édouard. Sur l'équation différentielle linéaire, qui admet pour intégrale la série hypergéométrique. Annales scientifiques de l'École Normale Supérieure, Série 2, Tome 10 (1881), pp. 3-142. (Pages supplémentaires) doi : 10.24033/asens.207. https://www.numdam.org/articles/10.24033/asens.207/
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- Extension of Chu–Vandermonde Identity and Quadratic Transformation Conditions, Axioms, Volume 13 (2024) no. 12, p. 825 | DOI:10.3390/axioms13120825
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- On a Generalization of the Kummer’s Quadratic Transformation and a Resolution of an Isolated Case, Axioms, Volume 12 (2023) no. 9, p. 821 | DOI:10.3390/axioms12090821
- Congruences corresponding to hypergeometric identities I. F12 transformations, Journal of Mathematical Analysis and Applications, Volume 505 (2022) no. 2, p. 125527 | DOI:10.1016/j.jmaa.2021.125527
- Hypergeometric functions over finite fields, Memoirs of the American Mathematical Society, Volume 280 (2022) no. 1382 | DOI:10.1090/memo/1382
- A new approach to hypergeometric transformation formulas, The Ramanujan Journal, Volume 55 (2021) no. 2, p. 793 | DOI:10.1007/s11139-020-00286-7
- An Accurate Analytic Mass Model for Lensing Galaxies, The Astrophysical Journal, Volume 892 (2020) no. 1, p. 62 | DOI:10.3847/1538-4357/ab7a15
- Asymptotic profile and optimal decay of solutions of some wave equations with logarithmic damping, Zeitschrift für angewandte Mathematik und Physik, Volume 71 (2020) no. 5 | DOI:10.1007/s00033-020-01373-x
- Extensions of the classical transformations of the hypergeometric function F23, Advances in Applied Mathematics, Volume 105 (2019), p. 25 | DOI:10.1016/j.aam.2019.01.002
- Iterative Non-iterative Integrals in Quantum Field Theory, Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory (2019), p. 51 | DOI:10.1007/978-3-030-04480-0_3
- Iterated elliptic and hypergeometric integrals for Feynman diagrams, Journal of Mathematical Physics, Volume 59 (2018) no. 6 | DOI:10.1063/1.4986417
- Resummation of Goldstone infrared divergences: A proof to all orders, Physical Review D, Volume 97 (2018) no. 5 | DOI:10.1103/physrevd.97.056020
- Hypergeometric expressions for generating functions of walks with small steps in the quarter plane, European Journal of Combinatorics, Volume 61 (2017), p. 242 | DOI:10.1016/j.ejc.2016.10.010
- Riemann Surfaces: Reception by the French School, From Riemann to Differential Geometry and Relativity (2017), p. 237 | DOI:10.1007/978-3-319-60039-0_8
- Hypergeometric series with gamma product formula, Indagationes Mathematicae, Volume 28 (2017) no. 2, p. 463 | DOI:10.1016/j.indag.2016.12.001
- The sixth Painlevé transcendent and uniformization of algebraic curves, Journal of Differential Equations, Volume 260 (2016) no. 3, p. 2507 | DOI:10.1016/j.jde.2015.10.009
- Goursat’s Hypergeometric Transformations, Revisited, Analytic Number Theory, Approximation Theory, and Special Functions (2014), p. 721 | DOI:10.1007/978-1-4939-0258-3_27
- Series for 1/π using Legendre's relation, Integral Transforms and Special Functions, Volume 25 (2014) no. 1, p. 1 | DOI:10.1080/10652469.2013.809072
- Euler–Goursat-like formula via Laplace–Borel duality, Journal of Mathematical Analysis and Applications, Volume 408 (2013) no. 2, p. 655 | DOI:10.1016/j.jmaa.2013.06.033
- 70+ Years of the Watson Integrals, Journal of Statistical Physics, Volume 145 (2011) no. 3, p. 591 | DOI:10.1007/s10955-011-0273-0
- A variant of Jacobi type formula for Picard curves, Journal of the Mathematical Society of Japan, Volume 62 (2010) no. 1 | DOI:10.2969/jmsj/06210305
- SU(2)-monopoles, curves with symmetries and Ramanujan's heritage, Sbornik: Mathematics, Volume 201 (2010) no. 6, p. 801 | DOI:10.1070/sm2010v201n06abeh004093
- A transformation formula for Appell's hypergeometric function
-
- Special Functions in Geometric Function Theory, Geometric Function Theory, Volume 2 (2005), p. 621 | DOI:10.1016/s1874-5709(05)80018-6
- Transformations of some Gauss hypergeometric functions, Journal of Computational and Applied Mathematics, Volume 178 (2005) no. 1-2, p. 473 | DOI:10.1016/j.cam.2004.09.053
- Flowers Which We Cannot Yet See Growing in Ramanujan’s Garden of Hypergeometric Series, Elliptic Functions, and q’S, Special Functions 2000: Current Perspective and Future Directions (2001), p. 61 | DOI:10.1007/978-94-010-0818-1_3
- Bibliography, Special Functions (1996), p. 349 | DOI:10.1002/9781118032572.biblio
- Ramanujan’s theories of elliptic functions to alternative bases, Transactions of the American Mathematical Society, Volume 347 (1995) no. 11, p. 4163 | DOI:10.1090/s0002-9947-1995-1311903-0
- Quadratic transformation formulas for basic hypergeometric series, Transactions of the American Mathematical Society, Volume 335 (1993) no. 1, p. 277 | DOI:10.1090/s0002-9947-1993-1074149-8
- Special values of the hypergeometric series, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 109 (1991) no. 2, p. 257 | DOI:10.1017/s0305004100069723
- Hyperelliptic integrals and multiple hypergeometric series, Mathematics of Computation, Volume 50 (1988) no. 182, p. 501 | DOI:10.1090/s0025-5718-1988-0929548-0
- The Stabilization Law for Transonic Flow, SIAM Journal on Applied Mathematics, Volume 46 (1986) no. 1, p. 27 | DOI:10.1137/0146004
- Transonic Far Fields, Transonic Aerodynamics, Volume 30 (1986), p. 182 | DOI:10.1016/b978-0-444-87958-5.50007-8
- Strange Evaluations of Hypergeometric Series, SIAM Journal on Mathematical Analysis, Volume 13 (1982) no. 2, p. 295 | DOI:10.1137/0513021
- The fundamental solution for the axially symmetric wave equation, Archive for Rational Mechanics and Analysis, Volume 67 (1977) no. 1, p. 83 | DOI:10.1007/bf00280829
- Analytic continuation of hypergeometric functions by complex single loop Euler transforms, Journal of Physics A: General Physics, Volume 5 (1972) no. 2, p. 256 | DOI:10.1088/0305-4470/5/2/008
- On long range effects in the motion of artificial satellites, Dynamics of Satellites / Dynamique des Satellites (1963), p. 21 | DOI:10.1007/978-3-642-48130-7_3
- A discussion of Halphen's method of secular perturbations and its application to the determination of long‐range effects in the motion of celestial bodies, Reviews of Geophysics, Volume 1 (1963) no. 1, p. 85 | DOI:10.1029/rg001i001p00085
- Sur le problème de Plateau pour un quadrilatère variable qui peut acquérir un point double, Annali di Matematica Pura ed Applicata, Volume 58 (1962) no. 1, p. 1 | DOI:10.1007/bf02413042
- Mathematical Notes, The American Mathematical Monthly, Volume 69 (1962) no. 9, p. 889 | DOI:10.1080/00029890.1962.11989999
- On the long-period lunisolar effect in the motion of the artificial satellite, Journal of Geophysical Research, Volume 66 (1961) no. 6, p. 1659 | DOI:10.1029/jz066i006p01659
- On regular and singular harmonic functions of three variables, Archive for Rational Mechanics and Analysis, Volume 4 (1959) no. 1, p. 352 | DOI:10.1007/bf00281396
- Risoluzione analitica delle equazioni algebriche generali, Rendiconti del Seminario Matematico e Fisico di Milano, Volume 29 (1959) no. 1, p. 13 | DOI:10.1007/bf02923187
- XXXIX.—Transformations of Hypergeometric Functions of Two Variables, Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, Volume 62 (1948) no. 3, p. 378 | DOI:10.1017/s0080454100006774
- Die Theorie der Integralgleichungen und die Darstellung willk�rlicher Funktionen in der mathematischen Physik, Mathematische Annalen, Volume 63 (1907) no. 4, p. 477 | DOI:10.1007/bf01449771
- Ueber verwandtes-Functionen, Mathematische Annalen, Volume 26 (1886) no. 1, p. 97 | DOI:10.1007/bf01443572
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