In mathematics, in the theory of ordinary differential equations in the complex plane , the points of are classified into ordinary points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction is made between a regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where the full solution set requires functions with higher growth rates. This distinction occurs, for example, between the hypergeometric equation, with three regular singular points, and the Bessel equation which is in a sense a limiting case, but where the analytic properties are substantially different.
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| - Punto fuchsiano (it)
- 정칙 특이점 (ko)
- Regular singular point (en)
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| - In mathematics, in the theory of ordinary differential equations in the complex plane , the points of are classified into ordinary points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction is made between a regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where the full solution set requires functions with higher growth rates. This distinction occurs, for example, between the hypergeometric equation, with three regular singular points, and the Bessel equation which is in a sense a limiting case, but where the analytic properties are substantially different. (en)
- 복소 상미분 방정식 이론에서, 정칙 특이점(正則特異點, 영어: regular singularity)은 선형 상미분 방정식의 해가 유리형 함수를 이루는 특이점이다. 정칙 특이점 근처에서는 프로베니우스 방법을 적용하여 미분 방정식의 해를 구할 수 있다. (ko)
- In matematica, nella teoria delle equazioni differenziali lineari di variabile complessa, un punto fuchsiano, anche detto singolarità fucsiana o punto singolare regolare, è un tipo particolare di punto singolare in corrispondenza del quale le soluzioni dell'equazione crescono non più velocemente di un polinomio. Il nome si deve a Lazarus Fuchs. Un'equazione differenziale ordinaria lineare omogenea definita nel piano complesso, di cui i coefficienti sono funzioni analitiche, è detta equazione fuchsiana se tutti i punti singolari sono punti fuchsiani sulla sfera di Riemann. (it)
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| - Fedoryuk (en)
- Il'yashenko (en)
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| - Fuchsian equation (en)
- Regular singular point (en)
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| - In mathematics, in the theory of ordinary differential equations in the complex plane , the points of are classified into ordinary points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction is made between a regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where the full solution set requires functions with higher growth rates. This distinction occurs, for example, between the hypergeometric equation, with three regular singular points, and the Bessel equation which is in a sense a limiting case, but where the analytic properties are substantially different. (en)
- 복소 상미분 방정식 이론에서, 정칙 특이점(正則特異點, 영어: regular singularity)은 선형 상미분 방정식의 해가 유리형 함수를 이루는 특이점이다. 정칙 특이점 근처에서는 프로베니우스 방법을 적용하여 미분 방정식의 해를 구할 수 있다. (ko)
- In matematica, nella teoria delle equazioni differenziali lineari di variabile complessa, un punto fuchsiano, anche detto singolarità fucsiana o punto singolare regolare, è un tipo particolare di punto singolare in corrispondenza del quale le soluzioni dell'equazione crescono non più velocemente di un polinomio. Il nome si deve a Lazarus Fuchs. Un'equazione differenziale ordinaria lineare omogenea definita nel piano complesso, di cui i coefficienti sono funzioni analitiche, è detta equazione fuchsiana se tutti i punti singolari sono punti fuchsiani sulla sfera di Riemann. (it)
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