Введение
Немецкий математик
Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a Jewish German mathematician who contributed important research in the field of linear differential equations. He was born in Moschin (Mosina) (located in Grand Duchy of Posen) and died in Berlin, Germany. He was buried in Schöneberg in the St. Matthew's Cemetery. His grave in section H is preserved and listed as a grave of honour of the State of Berlin. He is the eponym of Fuchsian groups and functions, and the Picard–Fuchs equation. A singular point a of a linear differential equation
is called Fuchsian if p and q are meromorphic around the point a,
and have poles of orders at most 1 and 2, respectively. According to a theorem of Fuchs, this condition is necessary and sufficient
for the regularity of the singular point, that is, to ensure the existence
of two linearly independent solutions of the form
where the exponents can be determined from the equation. In the case when
is an integer this formula has to be modified. Another well known result of Fuchs is the Fuchs's conditions, the necessary and sufficient conditions
for the non linear differential equation of the form
to be free of movable singularities. An interesting remark about him as a teacher during the period of his work at the Heidelberg University pertains to his manner of lecturing: his knowledge of the mathematics he was assigned to teach was so deep that he would not prepare before giving a lecture — he would simply improvise on the spot, while exposing the students to the train of thought taken by mathematicians of the finest degree. Lazarus Fuchs was the father of Richard Fuchs, a German mathematician.
Лазарь Эммануил Фукс (5 мая 1833 – 26 апреля 1902) был еврейским немецким математиком, внесшим значительный вклад в исследования в области линейных дифференциальных уравнений. Он родился в Мошине (Мосина) (расположенном в Великом герцогстве Позен) и умер в Берлине, Германия. Похоронен в Шёнеберге на кладбище Святого Матфея. Его могила в секции H сохранена и числится в списке почётных могил земли Берлин. Он является автором названий групп и функций Фукса, а также уравнения Пикара — Фукса. Сингулярная точка *a* линейного дифференциального уравнения называется фуксианской, если функции *p* и *q* мероморфны в окрестности точки *a* и имеют полюса порядков не выше 1 и 2 соответственно. Согласно теореме Фукса, это условие необходимо и достаточно для регулярности сингулярной точки, то есть для обеспечения существования двух линейно независимых решений вида, где показатели можно определить из уравнения. В случае, когда *n* является целым числом, эту формулу необходимо модифицировать. Другим известным результатом Фукса являются условия Фукса — необходимые и достаточные условия для нелинейного дифференциального уравнения вида, чтобы оно не имело подвижных сингулярностей. Интересный факт о нём как о преподавателе в период работы в Гейдельбергском университете касается его манеры лекций: его глубокое знание преподаваемой математики было настолько велико, что он не готовился к лекциям заранее — он просто импровизировал, демонстрируя студентам ход мыслей выдающихся математиков. Лазарь Фукс был отцом Ричарда Фукса, немецкого математика.
Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a Jewish German mathematician who contributed important research in the field of linear differential equations. He was born in Moschin (Mosina) (located in Grand Duchy of Posen) and died in Berlin, Germany. He was buried in Schöneberg in the St. Matthew's Cemetery. His grave in section H is preserved and listed as a grave of honour of the State of Berlin. He is the eponym of Fuchsian groups and functions, and the Picard–Fuchs equation. A singular point a of a linear differential equation
is called Fuchsian if p and q are meromorphic around the point a,
and have poles of orders at most 1 and 2, respectively. According to a theorem of Fuchs, this condition is necessary and sufficient
for the regularity of the singular point, that is, to ensure the existence
of two linearly independent solutions of the form
where the exponents can be determined from the equation. In the case when
is an integer this formula has to be modified. Another well known result of Fuchs is the Fuchs's conditions, the necessary and sufficient conditions
for the non linear differential equation of the form
to be free of movable singularities. An interesting remark about him as a teacher during the period of his work at the Heidelberg University pertains to his manner of lecturing: his knowledge of the mathematics he was assigned to teach was so deep that he would not prepare before giving a lecture — he would simply improvise on the spot, while exposing the students to the train of thought taken by mathematicians of the finest degree. Lazarus Fuchs was the father of Richard Fuchs, a German mathematician.
Избранные произведения
Über Funktionen zweier Variabeln, welche durch Umkehrung der Integrale zweier gegebener Funktionen entstehen, Гёттинген 1881 г. К теории линейных дифференциальных уравнений, Берлин 1901 г. Собрание сочинений, под редакцией Рихарда Фукса и Людвига Шлезингера. 3 тома. Берлин 1904–1909 гг.