Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is as the following limit: where r2(k) is a number of representations of k as a sum of the form a2 + b2 for integer a and b. It can be given in closed form as: where is Gauss's constant and is the Euler-Mascheroni constant. Another way to define/understand Sierpiński's constant is, Let r(n) denote the number of representations of by squares, then the Summatory Function of has the Asymptotic expansion , where is the Sierpinski constant. The above plot shows ,
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| - Sierpiński-Konstante (de)
- Constante de Sierpiński (fr)
- 시에르핀스키 상수 (ko)
- Sierpiński's constant (en)
- Stała Sierpińskiego (pl)
- Sierpińskis konstant (sv)
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| - Die Sierpiński-Konstante ist eine mathematische Konstante, benannt nach dem polnischen Mathematiker Wacław Sierpiński. Sie kann unter anderem durch den folgenden Ausdruck definiert werden: wobei die Anzahl der Darstellungen von in der Form mit ganzen Zahlen und unter Beachtung der Reihenfolge, die Kreiszahl und der natürliche Logarithmus ist. (de)
- La constante de Sierpiński est la constante mathématique, habituellement notée K, définie par : où r2(k) est le nombre de représentations de k comme une somme de deux carrés d'entiers. Sa valeur est : , où γ désigne la constante d'Euler-Mascheroni et Γ la fonction gamma. (fr)
- 시에르핀스키 상수(Sierpiński constant)는 바츠와프 시에르핀스키의 이름에서 명명되었으며, 시에르핀스키 상수는 대개 로 표시된 수학 상수다. 이를 정의하는 한 가지 방법으로는 제한된 표현식을 사용하는 것이다. 여기서 는 자연수 와 에 대한 형태 의 합인 의 표현 수다. 다음과 같이 닫힌 형식으로 제공 될 수 있다. 가우스 상수이고 오일러-마스케로니 상수이다. 감마 함수 (ko)
- Inom matematiken är Sierpińskis konstant en matematisk konstant, vanligen betecknad med K. Den definieras som gränsvärdet där r2(k) är antalet representationer av k som summan av två kvadrater. Den kan skrivas i sluten form som Konstanten är uppkallad efter Wacław Sierpiński. (sv)
- Stała Sierpińskiego – stała matematyczna oznaczana na ogół jako K, którą można zdefiniować jako granicę: gdzie wyraża, na ile sposobów można przedstawić jako dla i naturalnych. Jej przybliżona wartość wynosi: ≈ 2,58498 17595 79253 21706 58935... (pl)
- Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is as the following limit: where r2(k) is a number of representations of k as a sum of the form a2 + b2 for integer a and b. It can be given in closed form as: where is Gauss's constant and is the Euler-Mascheroni constant. Another way to define/understand Sierpiński's constant is, Let r(n) denote the number of representations of by squares, then the Summatory Function of has the Asymptotic expansion , where is the Sierpinski constant. The above plot shows , (en)
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| - Decimal expansion of Sierpiński's constant (en)
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| - Die Sierpiński-Konstante ist eine mathematische Konstante, benannt nach dem polnischen Mathematiker Wacław Sierpiński. Sie kann unter anderem durch den folgenden Ausdruck definiert werden: wobei die Anzahl der Darstellungen von in der Form mit ganzen Zahlen und unter Beachtung der Reihenfolge, die Kreiszahl und der natürliche Logarithmus ist. (de)
- La constante de Sierpiński est la constante mathématique, habituellement notée K, définie par : où r2(k) est le nombre de représentations de k comme une somme de deux carrés d'entiers. Sa valeur est : , où γ désigne la constante d'Euler-Mascheroni et Γ la fonction gamma. (fr)
- Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is as the following limit: where r2(k) is a number of representations of k as a sum of the form a2 + b2 for integer a and b. It can be given in closed form as: where is Gauss's constant and is the Euler-Mascheroni constant. Another way to define/understand Sierpiński's constant is, Let r(n) denote the number of representations of by squares, then the Summatory Function of has the Asymptotic expansion , where is the Sierpinski constant. The above plot shows , with the value of indicated as the solid horizontal line. (en)
- 시에르핀스키 상수(Sierpiński constant)는 바츠와프 시에르핀스키의 이름에서 명명되었으며, 시에르핀스키 상수는 대개 로 표시된 수학 상수다. 이를 정의하는 한 가지 방법으로는 제한된 표현식을 사용하는 것이다. 여기서 는 자연수 와 에 대한 형태 의 합인 의 표현 수다. 다음과 같이 닫힌 형식으로 제공 될 수 있다. 가우스 상수이고 오일러-마스케로니 상수이다. 감마 함수 (ko)
- Inom matematiken är Sierpińskis konstant en matematisk konstant, vanligen betecknad med K. Den definieras som gränsvärdet där r2(k) är antalet representationer av k som summan av två kvadrater. Den kan skrivas i sluten form som Konstanten är uppkallad efter Wacław Sierpiński. (sv)
- Stała Sierpińskiego – stała matematyczna oznaczana na ogół jako K, którą można zdefiniować jako granicę: gdzie wyraża, na ile sposobów można przedstawić jako dla i naturalnych. Jej przybliżona wartość wynosi: ≈ 2,58498 17595 79253 21706 58935... (pl)
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