The Mathematician Sophus Lie 2002
DOI: 10.1007/978-3-662-04386-8_13
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“…Thus Abel and Jacobi are recognized jointly for developing the theory of the elliptic functions in their current form [21]. A "noble competition" between these two young men may have developed [21], but subsequent polemics about the unquestionable priority of Abel and the alleged speculation that Jacobi may have been unfair and not cognizant of Abel's original contribution ( [28], [29]) may be countered if one recalls that on March 14, 1829, nearly a month before Abel's death, Jacobi wrote to Legendre [16] "Quelle découverte de M. Abel que cette généralisation de l'intégrale d'Euler! A-t-on jamais vu pareille chose!…”
Section: Copyright C 2005 By L Rosati and M C Nuccimentioning
confidence: 99%
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“…Thus Abel and Jacobi are recognized jointly for developing the theory of the elliptic functions in their current form [21]. A "noble competition" between these two young men may have developed [21], but subsequent polemics about the unquestionable priority of Abel and the alleged speculation that Jacobi may have been unfair and not cognizant of Abel's original contribution ( [28], [29]) may be countered if one recalls that on March 14, 1829, nearly a month before Abel's death, Jacobi wrote to Legendre [16] "Quelle découverte de M. Abel que cette généralisation de l'intégrale d'Euler! A-t-on jamais vu pareille chose!…”
Section: Copyright C 2005 By L Rosati and M C Nuccimentioning
confidence: 99%
“…It is well-known that Sophus Lie (1842-1899) was influenced by Abel's and especially Galois' work on algebraic equations as well as Jacobi's work on partial differential equations [13], [14]. Less well-known 2 may be his involvement with the republication of Abel's work [2] and unfruitful search for Abel's original manuscript [29] that Jacobi prized so much and went unnoticed and was subsequently lost at the Paris Academy 3 . In this paper we apply Lie group analysis to Jacobi's modular differential equation, which he derived for linking two different moduli of an elliptic integral [18], and obtain a six-dimensional Lie symmetry algebra isomorphic to sl(2, IR) × sl(2, IR) which transforms it into the well-known Schwarzian differential equation [15].…”
Section: Copyright C 2005 By L Rosati and M C Nuccimentioning
confidence: 99%